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Question

If any tangent to the ellipse x2a2+y2b2=1 intercepts equal length l on the axes, then l=

A
a2+b2
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B
(a2+b2)
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C
(a2+b2)2
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D
None of these
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Solution

The correct option is B (a2+b2)
Ellipse:x2a2+y2b2=1(i)
Tangent at any point on (i) be y=mx+a2m2+b2
Intercept formya2m2+b2+xa2m2+b2(m)=1
intercept at xaxis= that on yaxis
a2m2+b2m=a2m2+b2
m=1
so intercept length l=a2m2+b2
=a2(1)2+b2
=a2+b2

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