if $2$ hyperbola are conjugates of each other then value of $c$ If the hyperbola $x^2+3xy+2y^2+2x+3y+2=0$ and $x^2+3xy+2y^2+2x+3y+c=0$ are conjugate of each other . Then $c$ equals  solution i try   Asymptotes of 1 st hyperbola is $x^2+3xy+2y^2+2x+3y+k=0$  and it represent $2$ pair of lines so its discriminant is zero .so i am getting $k=1$ How to solve it from that point
Finding the conjugate hyperbola Assume we are given a general proper hyperbola $  a_{11}x^2 + 2 a_{12} x y + a_{22} y^2 + 2 a_{13}x +2 a_{23}y + a_{33} = 0$ with  $D =\det \begin{pmatrix}   a_{11} &amp; a_{12} \\   a_{12} &amp; a_{22} \end{pmatrix} &lt; 0$ and $ A = \det \begin{pmatrix}   a_{11} &amp; a_{12} &amp; a_{13} \\   a_{12} &amp; a_{22} &amp; a_{23} \\   a_{13} &amp; a_{23} &amp; a_{33} \end{pmatrix} \neq 0$.  Is there an easy way to find the implicit description of the conjugate hyperbola?  I could translate and rotate the hyperbola and obtain a canonical representation of the form $\frac{x^2}{a^2} - \frac{y^2}{b^2} = \pm 1$, find the conjugate of the canonical one and the transform back. However, I'm looking for a more straightforward way to achieve this.
Are there any non-green, non-artifact mana ramp cards? I have looked and can't seem to find any.  I have seen many green cards and some artifacts that do this, but nothing in Red, Blue, Black or White.    Are there any?  Note: By "Mana Ramp" I mean a card that generates mana, or one that lets you play more than one land per turn.  The end result, for example, would be on turn 4, playing a white only deck, I could tap more than 4 mana.  (Normally you only get one land per turn so a max of 4 mana on turn 4.) I would like to typeset the top part of Pascal's triangle. To get the triangle with the names of the binomial coefficients, i.e., {n \choose k}, I used the following code  \begin{tikzpicture} \foreach \n in {0,...,4} {   \foreach \k in {0,...,\n} {     \node at (\k-\n/2,-\n) {${\n \choose \k}$};   } } \end{tikzpicture}   The result is this   Now I want to be equally lazy and do something like this for the values of the binomial coefficients, i.e., replace {\n \choose \k} in the node label with \CalculateBinomialCoefficient{\n}{\k} where \CalculateBinomialCoefficient is a hypothetical macro that calculates the binomial coefficient. Has anyone done something like that?  The result should look like this: Every element of a group has order $2$. Why, intuitively, is it abelian? How to remove white space before reference? Indicate How Trustworthy the UpVotes Are Does excessive markup affect SEO? How to add a matrix to a LaTeX document How do we add a matrix to a LaTeX document? $k$ times's draw from $n$ numbers with replacement, each number at least appear once Sample $k$ times with order from $n$ distinct numbers with replacement where $k\ge n$. Here "with order" means the sample is treated like a sequence rather than a set, so results like "1,3,3" and "3,1,3" are different.  The question is what is the probability that every number is sampled at least once? My answer is $1-\frac{{\sum\limits_{i = 1}^n {C_n^i\times i! \times {{(n - i)}^k}} }}{{{n^k}}}$ where $C_n^i$ denotes $n$ chooses $i$.  ${C_n^i\times i! \times {{(n - i)}^k}}$ means first choose $i$ ($i=1,2,...,n-1$) of numbers not to appear in the sample, and then we sample from the remaining $n-i$ numbers for $k$ times.   My question is, is there more elegant solution where the numerator can be directly computed? i.e. can we directly calculate the number of possible sample sequences in which every number has at least one occurrence? Thank you!    PS: my attempt was $C_k^n\times n!\times n^{n-k}$, meaning that we first choose $n$ positions in the sequence of length $k$ to place $n$ numbers, and then permute the $n$ numbers. This is to ensure every number to appear once. The remaining $n-k$ are sampled from the $n$ numbers without restriction.   However, I later found this seems not correct, and it counts the same sequence multiple times.  PS2: as pointed out in the comments, my first answer "1- ..." is not correct either. PostGIS Geometry Query returns "Error: Operation on mixed SRID geometries" only for certain values How do I remove any Ubuntu brand and trademark from my Ubuntu install? I am running Ubuntu 17.10 and I would like to build a completely de-branded ISO of it. This means not just dropping the Ubuntu name from /etc/lsb_release but also deleting references in the text of the installation program, in the "about this computer" screen and so on.  I've already checked other questions but I do not consider them duplicate because:    is very old and it just turned into a bunch of "try this tool" suggestions  is also old and suggests a tool called relinux that hasn't seen updates in years  does mention APT packages (and I know how this works) but not trademarks   Therefore my questions are:   Starting from a stock Ubuntu 17.10 (or an official derivative), how can I remove references to the Ubuntu trademark and logo? What exact packages do I need to uninstall? Are there images I need to replace? Are there files I need to edit other than /etc/lsb_release?   Please note that I am not interested in removing other names such as Firefox. I am only interested in the name of the distro. How to make wget faster or multithreading? I've just upgraded my computer hardware(cpu + motherboard + graphic card + memory + hard disk), so that install a new OS is needed. I tried to download debian-6.0.6-amd64-netinst.iso with wget command but the speed is so slow that I could not bear. 4Kb/s ~ 17 Kb/s, slow like a running turtle, or even more slower if I use Chrome.  I've read the help information of wget, it seems like there are no options could make it more faster.  Is there anyway to make wget faster? Or is it possible to make it multi-threading download?  PS: my bandwidth is 4M. I use this command:  wget -c url  http://hammurabi.acc.umu.se/debian-cd/6.0.6/amd64/iso-cd/debian-6.0.6-amd64-netinst.iso Which Pokemon have the highest CP cap? It's clear that the evolved form of Pokemon have a far higher CP cap (and it looks like minimum too) but it would also seem there is a difference between different Pokemon.   For example I have an Oddish at 184 CP which is at 50% of it's cap, and I also have a Ratata at 185 CP but it is far closer to its cap, around 90%.  Which Pokemon have the highest CP caps? Sometimes I found that writing just "J. Doe" may lead, in a justified line with few words, to a big space between the initial and the surname. Using J.\,Doe looks ok but I would like to know if there is a general rule for spacing between initials and surnames. Print programs with its proper syntax I have defined my own language whose syntax is very close to the one of Pascal. I would like to type the following program for instance. Many people use the packages algorithmicx or algorithm2e to print programs, but it seems that we have to use their specific keywords of its syntax like procedure, end while.  I just want to indent spaces when needed, and bold some words when I want (sorry that I could not bold letters in the following figure). Do I have to use  texttt for each line? Also, with verbatim, I could not bold words...  Also, as the program is not large, I would need to put it on the left side of the page, and leave space for some explanasion text on its right hand side. So I  guss I need to get them all together, and use multicols.  Could anyone help?  program test                                      some text here var   i : integer;                                    ...    b : boolean; begin    i := 1;                                        ...    b := true;    while i &lt; 15 do       i := i  + 1;       b := not b                                  some text here    od end   Edit1: Following @Werner's tabbing solution, I have made the code a minipage:  \begin{minipage}[t]{0.48\linewidth}% \begin{tabbing} Werner's solution \end{tabbing} \end{minipage}\hfill \begin{minipage}[t]{0.48\linewidth} a paragraph \end{minipage}   Actually as the code shows, I want the texts to be another separated minipage on the right hand side of the code. I have then 2 questions:   is it reasonable to make 0.48\linewidth instead of 0.5\linewidth? 0.48\linewidth is a conventional choice? is it possible to make a frame around the code, and use \caption and \label to make it a reference (I prefer figures)? In my opinion the accepted answer should permanently stick as only the original question submitter has the ability to accept. Which movie/TV show has an evil cyborg harvesting eyes from androids in a hidden town? I watched it maybe more than 8 to 12 years ago, but as far as I remember there was this place where androids (or maybe they were cyborgs) lived. (I think it was more like a hidden town). This guy finds them by accident (or at least I remember it that way) and tries to help them. I don't remember seeing any aliens or spaceships or anything like that. It was live-action, and I think US-based.  So, what I remember:   The bad guy is a human who has one red flashy robotic eye (not like terminators, it looks like a square eye patch above one of his eyes that functions like a second eye), he is collecting eyes from these androids/cyborgs. He also kills some of these androids/cyborgs but not all of them, some of them he just collects their eyes and doesn't kill (or get to kill). There was this woman who was a sexbot or something, she tried to give pleasure to the bad guy at some point, yet the bad guy added one of her eyes to his collection instead, but didn't/wasn't able to kill her. Towards the end she says something like "I used to give pleasure, now I only want to give pain" The human guy who found them tried to help them defend themselves from the bad guys, but they were in bad shape, many of them needed repair. To repair some of them, they needed spare parts they didn't seem to have, but one of the android/cyborg dudes said something like "we don't really bury our dead" and he brought a box of spare parts (or maybe android/cyborg body parts), they used these parts to repair some of the androids/cyborgs. There was this android/cyborg guy who was an assassin or something, but lost his fingers or hands, they couldn't find any hands compatible to his, but he said something like "I can still feel my trigger finger, just attach the weapons to my hands".   I remember it as a great movie/tv show, but I can't find anything about it. Can someone help me?  Please and thank you in advance... How to round a number to n decimal places in Java What I would like is a method to convert a double to a string which rounds using the half-up method - i.e. if the decimal to be rounded is 5, it always rounds up to the next number. This is the standard method of rounding most people expect in most situations.  I also would like only significant digits to be displayed - i.e. there should not be any trailing zeroes.  I know one method of doing this is to use the String.format method:  String.format("%.5g%n", 0.912385);   returns:  0.91239   which is great, however it always displays numbers with 5 decimal places even if they are not significant:   String.format("%.5g%n", 0.912300);   returns:  0.91230   Another method is to use the DecimalFormatter:  DecimalFormat df = new DecimalFormat("#.#####"); df.format(0.912385);   returns:  0.91238   However as you can see this uses half-even rounding. That is it will round down if the previous digit is even. What I'd like is this:  0.912385 -&gt; 0.91239 0.912300 -&gt; 0.9123   What is the best way to achieve this in Java? Why is the time limit for editing comments 5 minutes? What is the reasoning behind this? In the movie Wonder Woman, we see Wonder Woman as a child who grows into an adult. During the same time we see the people around her - the Amazons - not seem to age at all. It's revealed that Wonder Woman is special.      She's actually a God and presumably immortal   The Amazons are, well, not quite human, but they aren't the same as WW.   It's also revealed that:      A long time ago there was a war between the Gods and all of them perished by the hands of Ares. Before Zeus died, he created Wonder Woman out of clay.   All of the Amazons have bronze aged weaponry and do not seem aware of the changes to the outside world. This suggests that they are several thousand years old.   Presumably Wonder Woman has a normal life span as a child and has just become an adult at the beginning of the film. This seems very incongruent to me. Maybe I missed something though.  So, does the film or the DC Extended Universe give any indication of how old Wonder Woman is? Or is my assumption that she's several thousand years old (based on the weaponry) correct, despite the apparent incongruity I brought up? I have the problem, that PHP replaces all spaces with underscores in POST and GET variables. For example if I have the URL: http://localhost/proxy.php?user name=Max the browser will convert it to http://localhost/proxy.php?user%20name=Max. But if I give the $_GET parameters out, the key is not user name but user_name (note the underscore)! Is there any possibility to change this behaviour?