The chord of contact of the tangents drawn fr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the point on the circle $x^2 + y^2 = a^2$ be $(a \cos 	heta, a \sin 	heta)$.The equation of the chord of contact of tangents drawn from $(a

Vedclass · Accepted Answer

$G.P.$

Vedclass · Answer

(B) Let the point on the circle $x^2 + y^2 = a^2$ be $(a \cos 	heta, a \sin 	heta)$.The equation of the chord of contact of tangents drawn from $(a \cos 	heta, a \sin 	heta)$ to the circle $x^2 + y^2 = b^2$ is given by $x(a \cos 	heta) + y(a \sin 	heta) = b^2$.This line touches the circle $x^2 + y^2 = c^2$.The perpendicular distance from the center $(0, 0)$ to the line $x(a \cos 	heta) + y(a \sin 	heta) - b^2 = 0$ must be equal to the radius $c$.So,$\frac{|-b^2|}{\sqrt{(a \cos 	heta)^2 + (a \sin 	heta)^2}} = c$.$\frac{b^2}{\sqrt{a^2(\cos^2 	heta + \sin^2 	heta)}} = c$.$\frac{b^2}{a} = c$,which implies $b^2 = ac$.Since $b^2 = ac$,the terms $a, b, c$ are in $G.P.$

The chord of contact of the tangents drawn from a point on the circle $x^2 + y^2 = a^2$ to the circle $x^2 + y^2 = b^2$ touches the circle $x^2 + y^2 = c^2$. Then $a, b, c$ are in:

Similar Questions

If the portion of the line $lx + my = 1$ falling inside the circle ${x^2} + {y^2} = {a^2}$ subtends an angle of $45^\circ$ at the origin,then

Find the equation of the pair of tangents drawn from the origin to the circle $x^2 + y^2 + 20(x + y) + 20 = 0$.

The range of values of $a$ such that the angle $\theta$ between the pair of tangents drawn from the point $(a, 0)$ to the circle $x^2 + y^2 = 1$ satisfies $\frac{\pi}{2} < \theta < \pi$ is :

Let a line perpendicular to the line $2x - y = 10$ touch the parabola $y^2 = 4(x - 9)$ at the point $P$. The distance of the point $P$ from the centre of the circle $x^2 + y^2 - 14x - 8y + 56 = 0$ is ...........

The sum of diameters of the circles that touch $(i)$ the parabola $75x^2 = 64(5y - 3)$ at the point $\left(\frac{8}{5}, \frac{6}{5}\right)$ and $(ii)$ the $y$-axis,is equal to $......$

Vedclass Test Series

Exam Paper Generator

Online Exam Module