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Question

lf the area of the quadrilateral formed by the tangent from the origin to the circle x2+y2+6x10y+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 c234c+64=0
AC=AB= Length of tangent from (0,0) to
S:x2+y2+6x10y+c=0
AC=AB=S1=c
Area of quadrilateral ABOC= Area of ABO+ Area of ACO
=12×AB×r+12×AC×r

=r2[c+c]
=rc
Given : rc=8
34c×c=8
34cc2=64
c234c+64=0

57220_33449_ans_114015f78e65453dbc4656df545a6331.png

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