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The curves $x^{2} + y^{2} + 6 x - 24 y + 72 = 0$ and $x^{2} - y^{2} + 6 x + 16 y - 46 = 0$ intersect in four point $P, Q$ , $R$ and $S$ lying on a parabola. Let $A$ be the focus of the parabola, then

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length of latusrectum is 8

Equation of directrix is $y + 1 = 0$

coordinates of A are (-3, 2)

vertex of the parabola is at (-3, 1)

answer is C, D.

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Detailed Solution

Add the two curve equations
2x² + 12x - 8y + 26 = 0
x² + 6x + 13 = 4y
(x + 3)² = 4(y - 1)

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