Engineering Board Exam Reviewer · Ellipses · medium

For any point on the ellipse 9x2+25y2=225, find the sum of its distances from the two foci.

1. 10
2. 5
3. 15
4. 8

Answer

A. 10

Solution

Divide by 225: x2/25+y2/9=1, so a=5. The sum of focal distances is 2a=10.

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1. Find the foci of the ellipse (x-2)2/25+(y+1)2/9=1.
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3. Find the equation of the ellipse with foci at ( 3,0) and a major axis of length 10.
4. Find the eccentricity of the ellipse x2/25+y2/9=1.
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6. Find the length of the major axis of the ellipse x2/25+y2/9=1.
7. Find the distance from the center of the ellipse x2/25+y2/9=1 to each directrix.
8. Find the area of the largest rectangle that can be inscribed in the ellipse x2/25+y2/9=1.
9. Find the distance between the foci of the ellipse 4x2+9y2-16x+18y-11=0.
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