The length of the latus rectum of the parabol | vedclass

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Question

(A) Given equation of the parabola is ${y^2} - 4y - 2x - 8 = 0$.Completing the square for the $y$ terms:${y^2} - 4y = 2x + 8$${y^2} - 4y + 4 = 2x + 8

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$2$

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(A) Given equation of the parabola is ${y^2} - 4y - 2x - 8 = 0$.Completing the square for the $y$ terms:${y^2} - 4y = 2x + 8$${y^2} - 4y + 4 = 2x + 8 + 4$${(y - 2)^2} = 2x + 12$${(y - 2)^2} = 2(x + 6)$.Comparing this with the standard form ${(y - k)^2} = 4a(x - h)$,we get $4a = 2$,which implies $a = 0.5$.The length of the latus rectum is given by $|4a|$.Therefore,the length of the latus rectum is $2$.

The length of the latus rectum of the parabola ${y^2} - 4y - 2x - 8 = 0$ is

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