Question 56 Answer and Explanation _ACT April 2019 Form B04 Math Section

56. Shown below is quadrilateralABCD inscribed in an ellipse. The figure will be placed in the standard (x, y) coordinate plane, and the ellipse will be described by the equation $\frac{{x}^{2}}{9}+\frac{{(y-5)}^{2}}{16}=1.$ Given that $\overline{AC}$ is the minor axis and $\overline{BD}$ is the major axis of the ellipse, what will be the coordinates of points A and B?

F. Point A:(-9,0); Point B:(0,16)

G. Point A:(-9,5); Point B:(0,21)

H. Point A:(-3,0); Point B:(0,4)

J. Point A:(-3,5); Point B:(0,9)

K. Point A:(-3,5); Point B:(4,5)

Answer and Explanation

Your Answer is

Correct Answer is J

Explanation

According to the ellipse coordinate equation, it can be seen that the center of the ellipse is at (0,5), the horizontal axis is the short axis, the short axis is 3, the vertical axis is the long axis, and the long axis is 4. So the coordinates of Point A are (0-3, 5), and the coordinates of Potint B are (0, 5+4), choose J