If A = {(x, y) : x^2 + y^2 = 25} and B = {(x, | vedclass

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(D) The set $A$ represents a circle with center $(0, 0)$ and radius $r = 5$. The equation is $x^2 + y^2 = 25$.The set $B$ represents an ellipse with t

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Four points

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(D) The set $A$ represents a circle with center $(0, 0)$ and radius $r = 5$. The equation is $x^2 + y^2 = 25$.The set $B$ represents an ellipse with the equation $x^2 + 9y^2 = 144$. Dividing by $144$,we get $\frac{x^2}{144} + \frac{9y^2}{144} = 1$,which simplifies to $\frac{x^2}{12^2} + \frac{y^2}{4^2} = 1$.This is an ellipse with semi-major axis $a = 12$ and semi-minor axis $b = 4$.Since the circle has a radius of $5$,and the ellipse has a minor axis of $4$ and a major axis of $12$,the circle intersects the ellipse at four distinct points because the circle's radius is greater than the semi-minor axis but less than the semi-major axis of the ellipse.Therefore,$A \cap B$ contains four points.

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

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