• # question_answer The focal chord of the parabola ${{(y-2)}^{2}}=16(x-1)$ is a tangent to the circle ${{x}^{2}}+{{y}^{2}}-14x-4y=51=0$, then slope of the focal chord can be A)  0                     B)  1 C)  2                                 D)  3

Correct Answer: B

Solution :

Focus of given parabola is (5, 2). Now any line through (5, 2) is (y - 2) = m (x - 5) This will be a tangent to the circle ${{(x-7)}^{2}}\,+{{(y-2)}^{2}}=2,$ If $\left| \frac{0-2m}{\sqrt{1+{{m}^{2}}}} \right|\,=\sqrt{2}\Rightarrow 4{{m}^{2}}\,=2+2{{m}^{2}}\Rightarrow \,m=\pm 1$

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