The co-ordinates of the extremities of the latus rectum of the parabola 5 y 2 = 4 x are Options: A . &nbsp ( 1 5 . 2 5 ) , ( − 1 5 , 2 5 ) B . &nbsp ( 1 5 . 2 5 ) , ( 1 5 , − 2 5 ) C . &nbsp ( 1 5 . 4 5 ) , ( 1 5 , − 4 5 ) D . &nbsp None of these

Answer: Option B : B y 2 = 4. 1 5 x ; a = 1 5 . Focus is ( 1 5 , 0 ) and co-ordinates of latus rectum are y 2 = 4 25 ⇒ y = ± 2 5 or end points of latus rectum are ( 1 5 , ± 2 5 ) .

The co-ordinates of the extremities of the latus rectum of the parabola 5y2=4x

Discussion Forum : Introduction To Conics And Parabola

Question -

The co-ordinates of the extremities of the latus rectum of the parabola $5 y^{2} = 4 x$ are

Options:

A .

(\frac{1}{5} . \frac{2}{5}), (\frac{- 1}{5}, \frac{2}{5})

B .

(\frac{1}{5} . \frac{2}{5}), (\frac{1}{5}, \frac{- 2}{5})

C .

(\frac{1}{5} . \frac{4}{5}), (\frac{1}{5}, \frac{- 4}{5})

D . None of these

Answer: Option B
:
B

$y^{2} = 4. \frac{1}{5} x; a = \frac{1}{5}$ . Focus is $(\frac{1}{5}, 0)$ and co-ordinates of latus rectum are $y^{2} = \frac{4}{25} \Rightarrow y = \pm \frac{2}{5}$

or end points of latus rectum are $(\frac{1}{5}, \pm \frac{2}{5})$ .

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