The Gateway to Computer Science Excellence
+1 vote

$x^4-3x^2+2x^2y^2-3y^2+y^4+2=0$ represents

  1. A pair of circles having the same radius
  2. A circle and an ellipse
  3. A pair of circles having different radii
  4. none of the above
in Others by
retagged by | 42 views

1 Answer

0 votes

$\begin{align}x^4-3x^2+2x^2y^2-3y^2+y^4+2&=0\\ \Rightarrow x^4+2x^2y^2+y^4-3(x^2+y^2)+2&=0\\ \Rightarrow (x^2+y^2)^2-3(x^2+y^2)+2&=0\\ \Rightarrow A^2-3A+2&=0 ~; ~[\mathrm{Let~}A=x^2+y^2] \\ \Rightarrow (A-1)(A-2)&=0 \\ \Rightarrow A&=1,2 \end{align}$

$\therefore x^2+y^2=1$ or $x^2+y^2=2$. So there are two circles with different radii.


So the correct answer is C.


Related questions

Quick search syntax
tags tag:apple
author user:martin
title title:apple
content content:apple
exclude -tag:apple
force match +apple
views views:100
score score:10
answers answers:2
is accepted isaccepted:true
is closed isclosed:true
52,345 questions
60,509 answers
95,349 users