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(B) The length of the tangent from a point $(x_1, y_1)$ to a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $\sqrt{x_1^2 + y_1^2 + 2gx_1 + 2fy_1 +

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$-4$

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(B) The length of the tangent from a point $(x_1, y_1)$ to a circle $x^2 + y^2 + 2gx + 2fy + c = 0$ is given by $\sqrt{x_1^2 + y_1^2 + 2gx_1 + 2fy_1 + c}$.Given the point $(5, 3)$ and the circle $x^2 + y^2 + 2x + ky + 17 = 0$,the length of the tangent is $7$.Substituting the values into the formula:$\sqrt{5^2 + 3^2 + 2(5) + k(3) + 17} = 7$$\sqrt{25 + 9 + 10 + 3k + 17} = 7$$\sqrt{61 + 3k} = 7$Squaring both sides:$61 + 3k = 49$$3k = 49 - 61$$3k = -12$$k = -4$.

If the length of the tangent drawn from the point $(5, 3)$ to the circle $x^2 + y^2 + 2x + ky + 17 = 0$ is $7$,then the value of $k$ is:

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