Question

Area of a quadrilateral formed by a pair of tangents from the point $(4,5)$ to the circle $x^2+y^2-4x-2y-11=0$ and a pair of its radii is

• A. $12$ sq. unit
• B. $4$ sq. unit
• C. $6$ sq. unit
• D. $8sq.unit$

Answer 1

The correct option is D $8sq.unit$

REF.Image.

C : $x^2+y^2-4x-2y-11=0$

centre (2,1)

$r=\sqrt{4+1+11}=4$

Area of the Quadrilateral PACB is

A = (Radius)$\times$ (Length of tangent)

Length of tangent $=\sqrt{4^2+5^2-16-10-11}$

$=\sqrt{16+25-16-21}$

$=\sqrt{4}$

$=2$

$\therefore A=4\times 2$

$\therefore A=8$ sq unit.