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# Find the equation of the parabola that satisfies the given conditions : Vertex (0,0); focus (3,0)

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

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A)
Toolbox:
• If the coordinates of focis is (a, 0) then the parabola is open rightward.
• The equaton of the parabola is $y^2=4ax$
Step 1 :
Given coordinates of the vertex is (0,0) and coordinates of focus is (3, 0)
Since the vertex of the parabola is (0,0) and also the focus lies on the positive x - axis.
The axis of the parabola is x - axis.
Hence the equation of the parabola is $y^2=4ax$
Substituting for $a$ we get,
$y^2=4(3)x$
$\Rightarrow y^2=12x$ is the required equation of the parabola.