The length of the latus rectum of the parabol | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(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+

Vedclass · Accepted Answer

$2$

Vedclass · Answer

(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

Similar Questions

What is the equation of the tangent to the curve $x^2 = -4y$ at the point $(-4, -4)$?

The number of common tangents to the parabolas $y = x^{2}$ and $y = -x^{2} + 4x - 4$ is:

Find the angle $\alpha$ between the tangents drawn from the point $(-2, -1)$ to the parabola $y^2 = 4x$. What is the value of $\tan \alpha$?

The equation of the tangent to the parabola $y = x^2 - x$ at the point where $x = 1$ is:

If the directrix of the parabola $x^2+4y-6x+\lambda=0$ is $y+1=0$,then which of the following is correct?

Vedclass Test Series

Exam Paper Generator

Online Exam Module