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प्रश्न
Find the vertex, focus, equation of directrix and length of the latus rectum of the following:
x2 – 2x + 8y + 17 = 0
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उत्तर
x2 – 2x = -8y – 17
(x – 1)2 = – 8y – 17 + 1
(x – 1)2 = – 8y – 16
(x – 1)2 = – 8(y + 2)
It is form of (x – h)2 = – 4a(y – k)
4a = 8
⇒ a = 2
(a) Vertex be (h, k) = (1, – 2)
(b) Foeus = (0 + h, – a + k)
= (0 + 1, – 2 – 2)
= (1, – 4)
(c) Equation of the directrix is y + k + a = 0
y – 2 + 2 = 0
y = 0
(d) Length of latus rectum is 4a
= 4 × 2
= 8 units
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