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Question
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
y2 – 4y – 8x + 12 = 0
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Solution
y2 – 4y = 8x – 12
(y – 2)2 = 8x – 12 + 4
= 8x – 8
= 8(x – 1)
(y – 2)2 = 8(x – 1)
It is form of (y – k)2 = Aa(x – h)
4a = 8
⇒ a = 2
(a) Vertex (h, k) = (1, 2)
(b) Focus = (a + h, 0 + k)
= (2 + 1, 0 + 2)
= (3, 2)
(c) Equation of the directrix x = – a + h
= – 2 + 1
= – 1
x + 1 = 0
(d) Length of latus rectum is
4a = 4 × 2
= 8 units.
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