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Question
Write the equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0.
Solution
The general equation of the parabola is (y − k)2 = 4a(x − h)
Here, the (h, k) = (−3,0)
Now, the directrix is given by
x = h − a
⇒ −5 = −3 − a [∵ x + 5 = 0 ⇒ x = −5]
⇒ a = 2
Hence, the equation is given by
(y − 0)2 = 4(2)(x + 3)
⇒ y2 = 8 (x + 3)
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