InterviewSolution
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InterviewSolution
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\left. \begin array l ( a , b ) \text and cuts orthogonally to circle x ^ 2 %2B y ^ 2 = \\ \text is \\ \text (a) 2 a x %2B 2 b y - ( a ^ 2 %2B b ^ 2 %2B p ^ 2 ) = 0 \\ \text (b) 2 a x %2B 2 b y - ( a ^ 2 - b ^ 2 %2B p ^ 2 ) = 0 \\ \text (c) x ^ 2 %2B y ^ 2 - 3 a x - 4 b y %2B ( a ^ 2 %2B b ^ 2 - p ^ 2 ) = 0 \\ \text (d) x ^ 2 %2B y ^ 2 - 2 a x - 3 b y %2B ( a ^ 2 - b ^ 2 - p ^ 2 ) = 0 \end array \right. |
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Answer» Let the centre be (α, β)∵It cut the circle x^2+ y^2= p^2orthogonally2(-α) × 0 + 2(-β) × 0 = c1 – p2c1 = p2Let equation of circle is x^2+ y^2- 2αx - 2βy + p2= 0It pass through (a, b) ⇒ a2+ b2- 2αa - 2βb + p2= 0Locus ∴ 2ax + 2by – (a^2+ b^2+ p^2) = 0. Option=A |
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