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  4. The length of the latus rectum of the parabola 4x2-4y+8x-1=0 is

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

NTA AbhyasNTA Abhyas 2022

Solution:

$4x^{2}-4y+8x-1=0$
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 $4b$ )