# Write the Equation of the Directrix of the Parabola X2 − 4x − 8y + 12 = 0. - Mathematics

Write the equation of the directrix of the parabola x2 − 4x − 8y + 12 = 0.

#### Solution

Given:
x2 − 4x − 8y + 12 = 0

$\Rightarrow \left( x - 2 \right)^2 - 4 - 8y + 12 = 0$
$\Rightarrow \left( x - 2 \right)^2 = 8\left( y - 1 \right) \left( 1 \right)$

Let Y = y−1, $X = x - 2$

∴ From (1), we have:

$X^2 = 8Y$

Comparing with $x^2 = 4ay$

$a = 2$

Directrix = Y = −a
⇒ − 1 = −a
⇒y = −a + 1
= −2 + 1
= −1

Therefore, the required equation of the directrix is $y = - 1$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 25 Parabola
Exercise 25.2 | Q 3 | Page 28