The length of the latus rectum of the parabol | vedclass

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

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$2$

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(B) Given equation of the parabola is $x^{2}+2y=8x-7$.Rearranging the terms,we get $x^{2}-8x=-2y-7$.Completing the square on the left side: $x^{2}-8x+16=-2y-7+16$.This simplifies to $(x-4)^{2}=-2y+9$.Factoring out $-2$ on the right side: $(x-4)^{2}=-2(y-\frac{9}{2})$.Comparing this with the standard form $(x-h)^{2}=4a(y-k)$,where the length of the latus rectum is $|4a|$.Here,$4a = -2$,so the length of the latus rectum is $|-2| = 2$.

The length of the latus rectum of the parabola $x^{2}+2y=8x-7$ is

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