20 points asap algebra ii

in the coordinate plane, let $f = (4,0).$ let $p$ be a point, and let $q$ be the projection of the point $p$ onto the line $x = \frac{25}{4}.$ the point $p$ traces a curve in the plane, so that
\[\frac{pf}{pq} = \frac{4}{5}\]for all points $p$ on the curve. find the area of the region formed by the curve.

The curve described described here is an ellipse with eccentricity , the ratio between the distance from the given focus F(4, 0) to any point Q along the directrix . Use this info to find the lengths of the semimajor and -minor axes, and . Then the area of the ellipse is .

the answer is b: 18

step-by-step explanation:

use the pythagorean theorem to .

a^2+b^2=c^2

plug 18 for "r"

the 2 legs are 18 and 24

18^2+24^2=c^2

324+576=c^2

900=c^2

c=30

30-12=18

18 is the radius

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