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Question

The equation of the parabola whose vertex is (−3,0) and directrix is x+5=0, is

A
x2=8(y+3)
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B
y2=8(x+3)
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C
x2=8(y3)
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D
y2=8(x3)
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Solution

The correct option is B y2=8(x+3)

A line passing through the vertex (3,0) and perpendicular to directrix x+5=0 is the axis of the parabola by definition which is xaxis.
Let focus of the parabola be (a,0).
Since vertex is the middle point of (5,0) and focus F(a,0),
3=(a5)2a=1Focus=(1,0)
Thus, the equation the parabola is
(x+1)2+y2=(x+5)2y2=8(x+3)

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