If A= (x, y): x2+y2=25 and B= (x, y): x2+y2=144 ; then A ∩ B contains

Question

If A= (x, y): x2+y2=25 and B= (x, y): x2+y2=144 ; then A ∩ B contains (A) one point (B) three points (C) two points (D) four points

Tardigrade Admin · Accepted Answer

Clearly, A is the set of all points on the circle x2+y2=25 and B is the set of all points on the ellipse x2+9 y2=144. These two intersect at four points P, Q, R and S. <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/fffbb00a2fa4c9b79947003f0b8fe0cf-.png" /> Hence, A ∩ B contains four points.

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

one point

three points

two points

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

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

Q. If A={(x,y):x2+y2=25} and B={(x,y):x2+y2=144}; then A∩B contains