Question

The equations of the tangents drawn from the origin to the circle $x^2+y^2-2rx-2hy+h^2=0$ are

• A. x = 0, y = 0
• B. $(h^2-r^2)x-2rhy=0,x=0$
• C. y = 0, x = 4
• D. $(h^2-r^2)x+2rhy=0,x=0$

Answer 1

The correct option is B $(h^2-r^2)x-2rhy=0,x=0$

The equation of tangents is $S{S}_1=T^2$
$\Rightarrow h^2(x^2+y^2-2rx-2hy+h^2)=(rx+hy-h^2{)}^2$
$\Rightarrow (h^2-r^2)x^2-2rhxy=0\Rightarrow x(h^2-r^2)x-2rhy=0$
$\Rightarrow x=0,(h^2-r^2)x-2rhy=0.$