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Question

The directrix of the parabola x2 − 4x − 8y + 12 = 0 is
(a) y = 0
(b) x = 1
(c) y = − 1
(d) x = − 1

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Solution

(c) y = −1

Given:
x2 − 4x − 8y + 12 = 0
x-22-4-8y+12=0x-22=8y-8x-22=8y-1

Putting X = x − 2, Y = y − 1:

X2=8Y

Comparing with X2=4aY:
a = 2

Equation of the directrix:
Y=-a
Y=-2
y-1=-2y=-2+1y=-1

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