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Question

If the area of the quadrilateral formed by the tangents from the origin to the circle x2+y2+6x10y+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 D 25
x2+y2+6x10y+c=0
For the given circle, radius r=9+25c
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 =Lr
15=c×9+25cc234c+225=0c=9,25

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