1
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Question

# S(3,4) and Sâ€²(9,12) are the foci of an ellipse and the foot of the perpendicular from S to a tangent to the ellipse is (1,âˆ’4). Then the eccentricity of the ellipse is:

A
313
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B
413
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C
513
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D
713
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Solution

## The correct option is C 513Given foci are S(3,4) and S′(9,12) and foot of the perpendicular from S to a tangent to the ellipse is (1,−4).We know that distance between foci is 2ae=√(9−3)2+(12−4)2=√36+64=10.........(1), where e is eccentricity of ellipse.2a is the length of major axis of ellipse. Center of ellipse is (6,8).We know that distance between center and foot of perpendicular to tangent is CP=a⟹a=√(6−1)2+(8−(−4))2=√25+144=13.From(1), we get eccentricity e=513.

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