Browse Questions

# Find the equation of the parabola that satisfies the given conditions : Focus (0,–3); directrix y = 3

$\begin {array} {1 1} (A)\;x^2=12y & \quad (B)\;y^2=12x \\ (C)\;x^2=-12y & \quad (D)\;y^2=-12x \end {array}$

Toolbox:
• If the coordinates of the focus is (0, -a) then the parabola is open downwards. The equation of the parabola is $x^2=-4ay$
Step 1 :
Given focus is (0, -3)
Given equation of directrix is y=3
Since the focus lie on the negative side of y - axis. The axis of the parabola is y - axis.
Hence the equation of the parabola is
$x^2=-4ay$
Substituting for $a$ we get,
$x^2=4(-3)y$
$\Rightarrow x^2=-12y$ is the equation of the parabola.