(D) The equation of the chord of contact from a point $(x_1, y_1)$ to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $xx_1 + yy_1 + g(x + x_1)

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(D) The equation of the chord of contact from a point $(x_1, y_1)$ to the circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $xx_1 + yy_1 + g(x + x_1) + f(y + y_1) + c = 0$.Given the point $(x_1, y_1) = (2, -3)$ and the circle $x^2 + y^2 + 4x - 6y - 12 = 0$,we have $g = 2$,$f = -3$,and $c = -12$.Substituting these values into the formula:$x(2) + y(-3) + 2(x + 2) - 3(y - 3) - 12 = 0$$2x - 3y + 2x + 4 - 3y + 9 - 12 = 0$$4x - 6y + 1 = 0$

Class 11 Mathematics 10-1.Circle and System of Circles Chord of contact of tangent and common chord

Medium

Find the equation of the chord of contact of the tangents drawn from the point $(2, -3)$ to the circle $x^2 + y^2 + 4x - 6y - 12 = 0$.

A
$x - 2y + 4 = 0$
B
$2x - 3y + 4 = 0$
C
$2x + 4y + 3 = 0$
D
$4x - 6y + 1 = 0$

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10-1.Circle and System of Circles

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Chord of contact of tangent and common chord

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MediumTS EAMCET 2022

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Tangents are drawn from the point $(-1, -4)$ to the circle $x^2 + y^2 - 2x + 4y + 1 = 0$. The length of the corresponding chord of contact is:

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If the chord of contact of the point $P(1, 1)$ with respect to the circle $S = x^2 + y^2 + 4x + 6y - 3 = 0$ meets the circle $S = 0$ at $A$ and $B$,then the area of $\triangle PAB$ is

DifficultAP EAMCET 2023

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Find the equation of the chord of contact of the tangents drawn from the point $(2, -3)$ to the circle $x^2 + y^2 + 4x - 6y - 12 = 0$.

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