Q86 / 150 · MHT CET 2020 (13 Oct Shift 1) · Mathematics

The length of latus rectum of the parabola whose focus is at $(1,-2)$ and directrix is the line $x+y+3=0$ is

A
$8 \sqrt{2}$ units
Correct answer
B
$2 \sqrt{2}$ units
C
$\sqrt{2}$ units
D
$4 \sqrt{2}$ units

Solution

$\hat{f}^{(1,-2)}$ $x+y+3=0$ Distance of focus from $\text { Dizectrix }=22$ $\begin{array}{l} 1^{2} \text { distance } \\ =\frac{|1-2+3|}{\sqrt{2}} \\ =\sqrt{2} . \end{array}$ Length of L.R $=2 \sqrt{2}$

Hence, the correct answer is option: 'B'.

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