Question

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

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

Answer 1

Answer: (D)

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 $x^{2}+9 y^{2}=144$. These two intersect at four points $P, Q, R$ and $S$.

Hence, $A \cap B$ contains four points.