Question

The product of slope of tangents from point $(0,1)$ to circle $x^2+y^2-2x+4y=0$ is:

• A. $-1$
• B. $1$
• C. $-2$
• D. $2$

Answer 1

The correct option is A $-1$

Equation of circle is
$(x-1{)}^2+(y+2{)}^2=5$
angle between the tangent from point $(0,1)$ is
$={\tan }^{-1}\left(\frac{2Lr}{L^2-r^2}\right)$
$L=\sqrt{S_1}=\sqrt{5}=r$
$\therefore$ angle between the tangent from point $(0,1)$ is $\frac{\pi }{2}$
Hence product of their slopes will be $-1$