The lats rectum of a parabola whose directrix is x + y

Question -

The lats rectum of a parabola whose directrix is x + y - 2 = 0 and focus is (3,-4), is

Options:

A . -

3 \sqrt{2}

B .

3 \sqrt{2}

C .

\frac{- 3}{\sqrt{2}}

D .

\frac{3}{\sqrt{2}}

Answer: Option B
:
B

Distance between focus and directrix is

= $∣ ∣ ∣ \frac{3 - 4 - 2}{\sqrt{2}} ∣ ∣ ∣ = \frac{\pm 3}{\sqrt{2}}$

Hence latus rectum = $3 \sqrt{2}$

( Since latus rectum is two times the distance between focus and directrix ) .

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