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Question

# The area of the quadrilateral formed by the tangents from the point (4, 5) to the circle x2+y2âˆ’4xâˆ’2yâˆ’11=0 with the pair of radii through the points of contact of the tangents is ;

A
4 sq. units
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B
8 sq. units
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C
6 sq. units
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D
None
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Solution

## The correct option is B 8 sq. unitsGiven equation of circle is x2+y2−4x−2y−11=0Comparing it with general equation of circle i.e., x2+y2+2gx+2fy+c=0, we get,(−g,−f)=(2,1)Radius = √g2+f2−c=√4+1+11=4Length of subtangent from point (4,5) = √42+52−42−2×5−11=2 Area of quadrilateral = Length of subtangent × Radius of circle= 2 × 4= 8 sq. unitsHence, (B) is the correct answer.

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