The equation of the pair of tangents to the c | vedclass

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

Question

(B) The equation of the pair of tangents from a point $(x_1, y_1)$ to a circle $S = 0$ is given by $SS_1 = T^2$.Here,$S = x^2 + y^2 - 2x + 4y + 3 = 0$

Vedclass · Accepted Answer

$7x^2 + 23y^2 + 30xy + 66x + 50y - 73 = 0$

Vedclass · Answer

(B) The equation of the pair of tangents from a point $(x_1, y_1)$ to a circle $S = 0$ is given by $SS_1 = T^2$.Here,$S = x^2 + y^2 - 2x + 4y + 3 = 0$.For the point $(6, -5)$,$S_1 = (6)^2 + (-5)^2 - 2(6) + 4(-5) + 3 = 36 + 25 - 12 - 20 + 3 = 32$.The equation of the tangent $T$ at $(x, y)$ is $xx_1 + yy_1 - (x + x_1) + 2(y + y_1) + 3 = 0$.Substituting $(6, -5)$,we get $T = 6x - 5y - (x + 6) + 2(y - 5) + 3 = 5x - 3y - 13$.Now,$SS_1 = T^2$ becomes:$32(x^2 + y^2 - 2x + 4y + 3) = (5x - 3y - 13)^2$.Expanding both sides:$32x^2 + 32y^2 - 64x + 128y + 96 = 25x^2 + 9y^2 - 30xy - 130x + 78y + 169$.Rearranging the terms:$7x^2 + 23y^2 + 30xy + 66x + 50y - 73 = 0$.

The equation of the pair of tangents to the circle $x^2 + y^2 - 2x + 4y + 3 = 0$ from the point $(6, -5)$ is:

Similar Questions

What is the product formed when ethyl alcohol reacts with chlorine in the presence of $NaOH$?

The time period of a second's pendulum is $2\, s$. The spherical bob,which is empty from inside,has a mass of $50\, g$. This is now replaced by another solid bob of the same radius but having a mass of $100\, g$. The new time period will be .... $s$.

Which of the following reagents when heated with ethyl chloride,forms ethylene?

The number of angular and radial nodes of $4d$ orbital respectively are

If the system of equations $x + 2y - 3z = 1$,$(k + 3)z = 3$,and $(2k + 1)x + z = 0$ is inconsistent,then the value of $k$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module