If (5,12) and (24,7) are the focii of a conic passing through the origin, then find the eccentricity of the conic(adsbygoogle = window.adsbygoogle || []).push({});

Attempt:

Found the centre as (h,k), midpoint of the given points. (x-h)^2/a^2+(y-k)^2/b^2=1 i put x=0 and y=0 as it passes through the origin. from the equation e^2=1-(b^2/a^2) i got a relation between a and b. distance between the two given points equals 2a*e thereby giving the second relation, manipulating both the equations, i got a quadratic in e which i solved but it became tedious and finally i got the wrong answer.

Help would be appreciated!

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# Equation of Ellipse

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