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(B) Let the point be $(h, k)$. The length of the tangent from $(h, k)$ to a circle $S = 0$ is $\sqrt{S(h, k)}$.Since the lengths of the tangents are e

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$\left( -2, -\frac{5}{2} \right)$

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(B) Let the point be $(h, k)$. The length of the tangent from $(h, k)$ to a circle $S = 0$ is $\sqrt{S(h, k)}$.Since the lengths of the tangents are equal,the power of the point with respect to the three circles must be equal.Let $S_1 = x^2 + y^2 - 1 = 0$,$S_2 = x^2 + y^2 + 8x + 15 = 0$,and $S_3 = x^2 + y^2 + 10y + 24 = 0$.Equating $S_1 = S_2$:$x^2 + y^2 - 1 = x^2 + y^2 + 8x + 15$$-1 = 8x + 15$ $\Rightarrow 8x = -16$ $\Rightarrow x = -2$.Equating $S_1 = S_3$:$x^2 + y^2 - 1 = x^2 + y^2 + 10y + 24$$-1 = 10y + 24$ $\Rightarrow 10y = -25$ $\Rightarrow y = -\frac{5}{2}$.Thus,the required point is $\left( -2, -\frac{5}{2} \right)$.

The coordinates of the point from where the tangents drawn to the circles ${x^2} + {y^2} = 1$,${x^2} + {y^2} + 8x + 15 = 0$,and ${x^2} + {y^2} + 10y + 24 = 0$ are of the same length are:

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