The equations of the tangents drawn from the origin to the circle x2 + y2 + 2 rx + 2hy + h2 = 0, are

Question

The equations of the tangents drawn from the origin to the circle x2 + y2 + 2 rx + 2hy + h2 = 0, are (A) x = 0 (B) y = 0 (C) (h2 - r2)x-2rhy=0  (D) (h2 - r2)x+2rhy=0

Tardigrade Admin · Accepted Answer

Since, tangents are drawn from origin. So, the equation of tangent be

y = m x

\Rightarrow

Length of perpendicular from origin = radius

\Rightarrow \frac{∣ m r + h ∣}{m ^{2} + 1} = r

\Rightarrow m^{2} r^{2} + h^{2} + 2 m r h = r^{2} (m^{2} + 1)

\Rightarrow m = ∣ ∣ \frac{r ^{2} - h ^{2}}{2 r h} ∣ ∣, m = \infty

∴

Equation of tangents are

y = ∣ ∣ \frac{r ^{2} - h ^{2}}{2 r h} ∣ ∣ x, x = 0

Therefore (a) and (c) are the correct answers

Q. The equations of the tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 r x + 2 h y + h^{2} = 0,$ are

$x = 0$

$y = 0$

$(h^{2} - r^{2}) x - 2 r h y = 0$

$(h^{2} - r^{2}) x + 2 r h y = 0$

Q. The equations of the tangents drawn from the origin to the circle x2+y2+2rx+2hy+h2=0, are

x=0

y=0

(h2−r2)x−2rhy=0

(h2−r2)x+2rhy=0

Q. The equations of the tangents drawn from the origin to the circle $x^{2} + y^{2} + 2 r x + 2 h y + h^{2} = 0,$ are

$x = 0$

$y = 0$

$(h^{2} - r^{2}) x - 2 r h y = 0$

$(h^{2} - r^{2}) x + 2 r h y = 0$