If the power of the point (1, 6) with respect | vedclass

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Question

(D) The power of a point $(x_1, y_1)$ with respect to a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $S_1 = x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c$.

Vedclass · Accepted Answer

$21$

Vedclass · Answer

(D) The power of a point $(x_1, y_1)$ with respect to a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $S_1 = x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c$. Given the point $(1, 6)$ and the circle $x^2 + y^2 + 4x - 6y - a = 0$,the power is $-16$. Substituting the values: $(1)^2 + (6)^2 + 4(1) - 6(6) - a = -16$ $1 + 36 + 4 - 36 - a = -16$ $5 - a = -16$ $-a = -16 - 5$ $-a = -21$ $a = 21$ Thus,the correct option is $D$.

If the power of the point $(1, 6)$ with respect to the circle $x^2 + y^2 + 4x - 6y - a = 0$ is $-16$,then $a =$

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