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

The length of latus -rectum of the parabola $x^{2}+2 y=8 x-7$ is
  1. 8
  2. 2
  3. 6
  4. 4

Solution

We have, $\begin{array}{l} x^{2}+2 y=8 x-7 \\ x^{2}-8 x=-2 y-7 \\ x^{2}-8 x+16=-2 y-7+16 \\ (x-4)^{2}=-2 y+9 \\ (x-4)^{2}=-2(y-9 / 2) \end{array}$ $\therefore$ Length of latus rectum $=2$

Asked in: MHT CET 2020 (16 Oct Shift 2)

Practice more Parabola questions on Aicharya