Find the equation of the parabola that satisfies the given conditons:
Focus (6,0); directrix x = -6

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Solution

Since the focus (6,0) lies on the x axis, therefore x - axis is the axis of parabola.
Also the directrix is x = -6 i.e. x = -a and focus (6,0) i.e. (a,0). So the parabola is of the form $y^{2} = 4 a x .$
The required equation of parabola is
$y^{2} = 4 \times 6 x \Rightarrow y^{2} = 24 x .$

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