Question

If $A = \\{(x, y) : x^2 + y^2 = 25\\}$ and $B = \\{(x, y) : x^2 + 16y^2 = 144\\}$ then $A \cap B$ contains

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

Answer 1

Answer: (D)

four points

Answer 2

Given $x^2 + 16y^2 = 144$ $\Rightarrow \frac{x^{2}}{12^{2}}+\frac{y^{2}}{3^{2}} = 1$ (An ellipse whose major axis is $x$-axis) $\quad\ldots\left(A\right)$ and $x^{2} + y^{2} = 25$ (a circle with radius $r = 5$ units) $\quad \ldots\left(B\right)$ From the graph of $A$ and $B$, we note that $A \cap B$ have four points.