The equation of the pair of tangents drawn fr | vedclass

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

Question

(C) The equation of the pair of tangents from a point $(x_1, y_1)$ to a circle $S = 0$ is given by $SS_1 = T^2$. Given $S = x^2 + y^2 + 2x + 2y + 1 =

Vedclass · Accepted Answer

$3x^2 - 8xy + 3y^2 + 2x + 2y - 2 = 0$

Vedclass · Answer

(C) The equation of the pair of tangents from a point $(x_1, y_1)$ to a circle $S = 0$ is given by $SS_1 = T^2$. Given $S = x^2 + y^2 + 2x + 2y + 1 = 0$ and point $(1, 1)$. $S_1 = 1^2 + 1^2 + 2(1) + 2(1) + 1 = 1 + 1 + 2 + 2 + 1 = 7$. $T = x(1) + y(1) + (x + 1) + (y + 1) + 1 = 2x + 2y + 3$. Substituting these into $SS_1 = T^2$: $7(x^2 + y^2 + 2x + 2y + 1) = (2x + 2y + 3)^2$. $7x^2 + 7y^2 + 14x + 14y + 7 = 4x^2 + 4y^2 + 9 + 8xy + 12x + 12y$. Rearranging the terms: $3x^2 - 8xy + 3y^2 + 2x + 2y - 2 = 0$.

The equation of the pair of tangents drawn from the point $(1, 1)$ to the circle $x^2 + y^2 + 2x + 2y + 1 = 0$ is:

Similar Questions

If the tangent at $(1,7)$ to the curve $x^2=y-6$ touches the circle $x^2+y^2+16x+12y+C=0$,then $C=$

If $\theta$ is the angle between the pair of tangents drawn from a point $P(x_1, y_1)$ to the circle $S = x^2 + y^2 + 2gx + 2fy + c = 0$,then which of the following is true?

Let the lines $(2-i)z = (2+i)\bar{z}$ and $(2+i)z + (i-2)\bar{z} - 4i = 0$ (where $i^2 = -1$) be normal to a circle $C$. If the line $iz + \bar{z} + 1 + i = 0$ is tangent to this circle $C$,then its radius is

If the line $4x - 3y + 7 = 0$ touches the circle $x^2 + y^2 - 6x + 4y - 12 = 0$ at $(\alpha, \beta)$,then $\alpha + 2\beta =$

Let $AB$ be a chord of length $12$ of the circle $(x-2)^{2}+(y+1)^{2}=\frac{169}{4}$. If tangents drawn to the circle at points $A$ and $B$ intersect at the point $P$,then five times the distance of point $P$ from chord $AB$ is equal to $.......$

Vedclass Test Series

Exam Paper Generator

Online Exam Module