The equation of the directrix of the parabola | vedclass

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Question

(A) Given,the equation of the parabola is ${x^2} + 8y - 2x = 7$.Rearranging the terms,we get ${x^2} - 2x = -8y + 7$.Completing the square on the left

Vedclass · Accepted Answer

$y = 3$

Vedclass · Answer

(A) Given,the equation of the parabola is ${x^2} + 8y - 2x = 7$.Rearranging the terms,we get ${x^2} - 2x = -8y + 7$.Completing the square on the left side: ${x^2} - 2x + 1 = -8y + 7 + 1$.This simplifies to ${(x - 1)^2} = -8y + 8$.Factoring out $-8$,we get ${(x - 1)^2} = -8(y - 1)$.Comparing this with the standard form ${(x - h)^2} = -4a(y - k)$,where $(h, k) = (1, 1)$ and $4a = 8$,we find $a = 2$.The equation of the directrix for a downward-opening parabola is $y = k + a$.Substituting the values,$y = 1 + 2 = 3$.Therefore,the equation of the directrix is $y = 3$.

The equation of the directrix of the parabola ${x^2} + 8y - 2x = 7$ is

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