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Questions  >>  CBSE XI  >>  Math  >>  Conic Sections
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Q)

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

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

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A)
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.
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