Question

The y coordinates of all the points of intersection of the parabola $y^2=x+2$ and the circle $x^2+y^2=4$ are given by

• A. $2,-2$
• B. $0$
• C. $0,\sqrt{3},-\sqrt{3}$
• D. $1,2,-1$
• E. $1,-2,1$

Answer 1

Answer: (C)

$0,\sqrt{3},-\sqrt{3}$

$x^2+y^2=4$ & $y^2=x+2$

$\Rightarrow x^2+x+2=4$

$\Rightarrow x^2+x-2=0$

$\Rightarrow (x+2)(x-1)=0$

$\Rightarrow x=1,-2$

$\Rightarrow y^2=0$ for $x=-2$

$y^2=3$ for $x=1$

$\Rightarrow y=0,\pm \sqrt{3}$.