Question

Let $A=\{(x,y):x,yϵR,x^2{y}^2+y^2=1\}$ and $B=\{(x,0):xϵR,-1\le x\le 1\}.$ Then $A\cap B=\{(-a,0),(1,b)\}$ .Find relation between a and b

Answer 1

Given, $A=(x,y):x,yϵR,x^2{y}^2+y^2=1,B=(x,0):xϵR,-1\le x\le 1$
$A\cap B=(-a,0),(1,b)$
let the common point for A and b be $c=(p,q)$.
$\Rightarrow q=0$ (from condition B)
$\Rightarrow c=(p,0)$
On substituting c in A,
$p^2\times 0^2+0^2=1$
$0=1$ which is never possible.
$\therefore$ Intersection of A and B is nullset.