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Question

If chord contact of the tangents drawn from the point (α,β) to the ellipse x2a2+y2b2=1, touches the circle x2+y2=c2, THEN THE LOCUS OF THE POINT (α,β)

A
x2a2+y2b2=1c2
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B
x2a2+y2b2=1c4
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C
x2a4+y2b4=1c2
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D
none of these
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Solution

The correct option is B x2a2+y2b2=1c4
Equation of chord to the ellipse
x2a2+y2b2=1 from point (α,β) is xαa2+yβb2=1 (1)

As per question line(1) touches the circle x2+y2=c2
Perpendicular that is distance from(0,0) from line 1 is

0+01(αa2)2+(βb2)2=c

1α2a2+β2b2=c

α2a2+β2b2=1c2

Locus of point ( α,β)

x2a2+y2b2=1c2


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