Question

An elliptical mirror measures 20 inches wide and 24 inches high. The ellipse is centered at (0, 60) on a coordinate plane, where units are in inches. Which equation represents the mirror?

Answer 1

The height and width of the outline (perimeter) of the mirror, as well as the

center in relation to the plane of the edges are given.

$\displaystyle The \ mirror \ can \ be \ \mathbf{ represented} \ by \ the \ equation; \underline{\frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}$

Reasons:

Width of the elliptical mirror = 20 inches

Height of the elliptical mirror = 24 inches

Center of the ellipse = (0, 60)

The equation of an ellipse is;  $\displaystyle \mathbf{\frac{(x - h)^2}{b^2} + \frac{(y - k)^2}{a^2}} = 1$

Where;

(h, k) = Coordinates of the center;

a = Semi major axis

b = Semi minor axis

In the mirror, we have;

(h, k) = (0, 60)

a = 24 ÷ 2 = 12

b = 20 ÷ 2 = 10

Which gives;

$\displaystyle \frac{(x - 0)^2}{10^2} + \frac{(y - 60)^2}{12^2} = \frac{x ^2}{100} + \frac{(y - 60)^2}{144} = \mathbf{\frac{(y - 60)^2}{144} + \frac{x^2}{100}} = 1$

Therefore;

$\displaystyle The \ equation \ that \ represent \ the \ mirror \ is; \underline{ \frac{(y - 60)^2}{144} + \frac{x^2}{100} = 1}$

Learn more about the equation of an ellipse here:

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