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Question
Write the equation of the directrix of the parabola x2 − 4x − 8y + 12 = 0.
Solution
Given:
x2 − 4x − 8y + 12 = 0
\[ \Rightarrow \left( x - 2 \right)^2 = 8\left( y - 1 \right) \left( 1 \right)\]
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 \[y = - 1\]
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