The area (in sq. units) of the triangle formed by the two tangents drawn from the external point O(0,0) to the circle x2+y2-2 g x-2 h y+h2=0 and their chord of contact is

Question

The area (in sq. units) of the triangle formed by the two tangents drawn from the external point O(0,0) to the circle x2+y2-2 g x-2 h y+h2=0 and their chord of contact is (A) (g h/h3+g2) (B) (g h/h2+g3) (C) (h g3/h2+g2) (D) (g h3/h2+g2)

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/e11fcb794e10da06c2592dc01230e2ba-.png" /> We have, equation of circle is x2+y2-2 g x-2 h y+h2=0 ∴ Radius of circle, A C=√g2+h2-h2=g and Length of tangent, O A=√0+0-0-0+h2=h Now, in triangle O A C tan θ=(A C/O A)=(g/h) ∴ sin θ=(2 tan θ/1+ tan 2 θ)=(2 × (g/h)/1+(g2)h2)=(2 g h/h2+g2) ∴ Area of Δ O A B=(1/2) O A × O B × sin 2 θ =(1/2) × h × h × (2 g h/h2+g2)=(g h3/h2+g2)

Q. The area (in sq. units) of the triangle formed by the two tangents drawn from the external point $O (0, 0)$ to the circle $x^{2} + y^{2} - 2 gx - 2 h y + h^{2} = 0$ and their chord of contact is

$\frac{g h}{h ^{3} + g ^{2}}$

$\frac{g h}{h ^{2} + g ^{3}}$

$\frac{h g ^{3}}{h ^{2} + g ^{2}}$

$\frac{g h ^{3}}{h ^{2} + g ^{2}}$

Q. The area (in sq. units) of the triangle formed by the two tangents drawn from the external point O(0,0) to the circle x2+y2−2gx−2hy+h2=0 and their chord of contact is

h3+g2gh​

h2+g3gh​

h2+g2hg3​

h2+g2gh3​

Q. The area (in sq. units) of the triangle formed by the two tangents drawn from the external point $O (0, 0)$ to the circle $x^{2} + y^{2} - 2 gx - 2 h y + h^{2} = 0$ and their chord of contact is

$\frac{g h}{h ^{3} + g ^{2}}$

$\frac{g h}{h ^{2} + g ^{3}}$

$\frac{h g ^{3}}{h ^{2} + g ^{2}}$

$\frac{g h ^{3}}{h ^{2} + g ^{2}}$