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Find the equation of the parabola with f...

Find the equation of the parabola with focus at F(3,0) and the directrix x=-3.

Text Solution

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The focus of the parabola is `(3, 0)`.
Since, the ordinate of the focus is '0'. It lies on the x-axis.
Thus, x-axis itself is the axis of the parabola.
Hence, the required equation is either of the form `y^(2) = 4ax or y^(2) = -4ax`.
Since, the directrix is x = -3 and the focus is (3, 0)
`therefore` Required equation of the parabola is `y^(2) = 4(3)x`
i.e., `y^(2) = 12x`
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