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

• A

  one point
• B

  three points
• C

  two points
• Correct answer
  D

  four points

Solution

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.

Hence, the correct answer is option: 'D'.