Question

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

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

Answer 1

Answer: (A), (C)

Since, tangents are drawn from origin. So, the equation of tangent be $y = m x$
$\Rightarrow $ Length of perpendicular from origin = radius

$\Rightarrow \frac{| mr+h |}{\sqrt{m^2+1}}=r$
$\Rightarrow m^2r^2+h^2+2mrh=r^2(m^2+1)$
$\Rightarrow m=\Bigg|\frac{r^2-h^2}{2rh}\Bigg|, m=\infty$
$\therefore$ Equation of tangents are $y=\Bigg|\frac{r^2-h^2}{2rh}\Bigg|x,x=0$
Therefore (a) and (c) are the correct answers