Question

If $A=\left\{\right(x,y):x^2+y^2=25\}$ and $B=\left\{\right(x,y):x^2+9y^2=144\}$; then $A\cap B$ contains

• A. one point
• B. three points
• C. two points
• D. four points

Answer 1

The correct option is D four points

Clearly, $A$ is the set of all points on the circle $x^2+y^2=25$ and $B$ is the set of all points on the ellipse $x^2+9y^2=144$. These two intersect at four points $P,Q,R$ and $S$.
Hence, $A\cap B$ contains four points.