Question

The area of the quadrilateral formed by the tangents from the point (4, 5) to the circle $x^2+y^2-4x-2y-11=0$ with the pair of radii through the points of contact of the tangents is ;

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

Answer 1

The correct option is B 8 sq. units

Given equation of circle is $x^2+y^2-4x-2y-11=0$

Comparing it with general equation of circle i.e., $x^2+y^2+2gx+2fy+c=0$, we get,

$(-g,-f)=(2,1)$

Radius = $\sqrt{g^2+f^2-c}=\sqrt{4+1+11}=4$

Length of subtangent from point (4,5) = $\sqrt{4^2+5^2-4^2-2\times 5-11}=2$

Area of quadrilateral

= Length of subtangent $\times$ Radius of circle

= 2 $\times$ 4

= 8 sq. units

Hence, (B) is the correct answer.