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Question

If (5,12) and (24,7) are the foci of an ellipse passing through the origin, then the eccentricity of the conic is

A
38612
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B
38613
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C
38625
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D
38638
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Solution

The correct option is C 38638
Let S(5,12),S(24,7) be the two foci.

P(0,0) is a point on the conic.

SP=25+144=13

SP=576+49=625=25

SS=(245)2+(712)2=192+52=386

If the conic is an ellipse, then

SP+SP=2a and SS=2ae

e=SSSP+SP=38613+25=38638


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