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Column-I Column-II
A) The equation of a common tangent to the circles $x^{2} + y^{2} - 12 x - 8 y + 27 = 0$ and $x^{2} + y^{2} + 4 x + 4 y - 17 = 0$ is P) $5 x - 5 y - 9 = 0$
B) The equation to the chord of $y^{2} = 16 x$ whose middle point $(4, 2)$ is Q) $x - y + 5 = 0$
C) The equation of tangent from $(- 4, 1)$ to $9 x^{2} + 16 y^{2} = 144$ is R) $4 x + 3 y - 11 = 0$
D) The centre of rectangular hyperbola lies on $y = 4 x$ and one of the asymptote is $x + y + 3 = 0$ then the other asymptote is S) $4 x - y - 14 = 0$

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$A - R; B - Q; C - P; D - S$

$A - S; B - R; C - Q; D - P$

$A - R; B - S; C - P; D - Q$

$A - R; B - S; C - Q; D - P$

answer is D.

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Detailed Solution

A. Circle touch each other $∴$ $S - S^{1} = 0$ is a common tangent
B. $S_{1} = S_{\prod}$
C. $y - 1 = m (x + 4)$ is tangent if ${(4 m + 1)}^{2} = 16 m^{2} + 9$
D.Center is point of intersection of $y = 4 x$ and $x + y + 3 = 0$ and other asymptotes also passes through centre $(\frac{- 3}{5}, \frac{- 12}{5})$ and perpendicular $x + y + 3 = 0$ .

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