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(y−3)
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D
y2=8(x−3)
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Solution
The correct option is By2=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 x−axis.
Let focus of the parabola be (a,0).
Since vertex is the middle point of (−5,0) and focus F(a,0), ∴−3=(a−5)2⇒a=−1∴Focus=(−1,0)
Thus, the equation the parabola is (x+1)2+y2=(x+5)2⇒y2=8(x+3)