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Let $3 x - y - 8 = 0$ be the equation of tangent to a parabola at the point $(7, 13)$ . If the focus of the parabola is at $(- 1, - 1)$ then its directrix is

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x - 8y + 19 = 0

8x + y + 19 = 0

8x - y + 19 = 0

x + 8y +19 = 0

answer is D.

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Detailed Solution

Find image M of. focus wrt tangent. we get M = (5, -3)
slope of (PM) - $θ$
slope of directrix is 1/8
M lies on directrix.
Equation of directrix is x + 8y + 19 = 0

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