If the area of the quadrilateral formed by the tangents from the origin to the circle x2+y2+6x−10y+c=0 and radii corresponding to the point of contact is 15 sq. units, then value(s) of c can be
A
5
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B
9
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C
16
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D
25
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Solution
The correct option is D25 x2+y2+6x−10y+c=0
For the given circle, radius r=√9+25−c
Now (0,0) should lie outside the circle.
Hence c>0
Length of tangent from (0,0) to the circle is L=√c
So, required area is =L⋅r 15=√c×√9+25−c⇒c2−34c+225=0⇒c=9,25