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Question

If the area of the quadrilateral formed by the tangent from the origin to the circle x2+y2+6x−10y+c=0 and the pair of radii at the points of contact of these tangents to tbe circle is 8 square units. then c is a root of the equation

A
c232c+64=0.
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B
c234c+64=0.
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C
c2+2c64=0.
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D
c2+34c64=0.
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Solution

The correct option is A c234c+64=0.
Let OA,OB be the tangents from the origin to the given circle with centre C(3,5)
and radius .9+25c=34c
Then area of the quadribiteral OACB=2× area of OAC=2×(12)×OA×AC
Now OA= length of the tangent from the origin to the given circle =.C
and AC= radius of the circle =34c so that. C34c=8 ...(given)
c(34c)=64c234c+64=0

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