Question

Equation of pair of tangents drawn from $(4,3)$ to the circle $x^2+y^2=4$ is

• A. $5x^2+12y^2+24xy-32x+24y-100=0$
• B. $5x^2+12y^2-24xy+32x+24y-100=0$
• C. $5x^2+12y^2-24xy-32x+24y+100=0$
• D. $5x^2+12y^2+24xy+16x+24y-100=0$

Answer 1

The correct option is B $5x^2+12y^2-24xy+32x+24y-100=0$

$S:x^2+y^2-4$
$S_1:4^2+3^2-4=21$
$T:4x+3y-4$
Equation of pair of tangents is
$S{S}_1=T^2$
$\Rightarrow 21(x^2+y^2-4)=(4x+3y-4{)}^2$
$\Rightarrow 21x^2+21y^2-84=16x^2+9y^2+16+24xy-24y-32x$
$\Rightarrow 5x^2+12y^2-24xy+32x+24y-100=0$