Question

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

Answer 1

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

Therefore, the required equation of the directrix is \[y = - 1\]