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The point on y^(2)=4ax nearest to the fo...

The point on `y^(2)=4ax` nearest to the focus has to abscissa equal to

A

`-a`

B

`a`

C

`a//2`

D

`0`

Text Solution

Verified by Experts

The correct Answer is:
D
Let `P(at^(2), 2at)` be a point on the parabola `y^(2)=4ax` and S be the focus of the parabola. Then,
`SP=a+at^(2)" "[because"Focal distaance"=x+a]`
Clearly, SP is least for t = 0.
Hence, the abscissae of P is `at^(2)=axx0=0`.
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