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Question
The equation of the directrix of the parabola x2 + 8y – 2x – 7 = 0 is __________.
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Solution
Given equation of parabola is,
x2 + 8y − 2x − 7 = 0
i.e. x2 − 2x + 8y − 7 = 0
i.e. x2 − 2x + 1 + 8y − 7 − 1 = 0
i.e. (x − 1)2 = − 8y + 8
i.e. (x − 1)2 = − 8(y − 1) = −4(2) (y − 1)
∴ equation of directrix is given by y − 1 = 2
i.e. y = 1 + 2 = 3
x2 + 8y − 2x − 7 = 0
i.e. x2 − 2x + 8y − 7 = 0
i.e. x2 − 2x + 1 + 8y − 7 − 1 = 0
i.e. (x − 1)2 = − 8y + 8
i.e. (x − 1)2 = − 8(y − 1) = −4(2) (y − 1)
∴ equation of directrix is given by y − 1 = 2
i.e. y = 1 + 2 = 3
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