Question 51 Answer and Explanation _ACT June 2018 Form A11 Math Section

51. Shown below in the standard (x,y) coordinate plane are 2 circles and 1 ellipse, each centered at (0,0). The larger circle has equation x² + y² = 25 and intersects the ellipse at exactly 2 points, both on the x-axis. The smaller circle has equation x² + y² = 4 and intersects the ellipse at exactly 2 points, both on the y-axis. Which of the following equations represents the ellipse?

A. $\frac{{x}^{2}}{2}+\frac{{y}^{2}}{5}=1$

B. $\frac{{x}^{2}}{4}+\frac{{y}^{2}}{25}=1$

C. $\frac{{x}^{2}}{5}+\frac{{y}^{2}}{2}=1$

D. $\frac{{x}^{2}}{25}+\frac{{y}^{2}}{4}=1$

E. $\frac{{x}^{2}}{100}+\frac{{y}^{2}}{16}=1$

Answer and Explanation

Your Answer is

Correct Answer is D

Explanation

Because the ellipse is longer in the x-axis direction than the y-axis direction, and the radius of the big circle is 5 and the radius of the small circle is 2, choose D