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Question: The equation of the directrix of the parabola x<sup>2</sup> + 8y – 2x = 7 is –...

The equation of the directrix of the parabola x2 + 8y – 2x = 7 is –

A

y = 3

B

y = – 3

C

y = 2

D

y = 0

Answer

y = 3

Explanation

Solution

x2 + 8y – 2x = 7

̃ x2 – 2x + 1 = –8y + 7 + 1

̃ (x – 1)2 = –8(y – 1) ...(1)

(x – x1)2 = –4a(y – y1) ...(2)

̃ 4a = 8 ̃ a = 2 Compare eq.(1) & (2)

Vertex A(x1, y1) = (1, 1) Q AQ = AS = 'a' = 2

Q{y1 = 1 + AQ = 1 + 2 = 3}\ eq. of dire. is

̃ y = y1 ̃ y = 3