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Question

# lf 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 the 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 B c2−34c+64=0AC=AB= Length of tangent from (0,0) toS:x2+y2+6x−10y+c=0AC=AB=√S1=√cArea of quadrilateral ABOC= Area of △ABO+ Area of △ACO=12×AB×r+12×AC×r=r2[√c+√c]=r√cGiven : r√c=8√34−c×√c=8⇒34c−c2=64⇒c2−34c+64=0

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