Question

The length of the latus rectum of the parabola $4x^2-4y+8x-1=0$ is

Answer 1

Answer: 1

$4x^2-4y+8x-1=0$
Rewriting the given equation of parabola similar to standard form,
$\Rightarrow 4{\left(x+1\right)}^2=4y+5$
$\Rightarrow {\left(x+1\right)}^2=\left(y+\frac{5}{4}\right)$
This is of form $x^2=4by$
$\Rightarrow L.R.=1$ (length of the Latus Rectum of $x^2=4by$ is $4b$ )