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A point on the parabola y^2=18 x at whic...

A point on the parabola `y^2=18 x` at which the ordinate increases at twice the rate of the abscissa is (a) (2,6) (b) `(2,-6)` `(9/8,-9/2)` (d) `(9/8,9/2)`

A

`(9//8,9//2)`

B

(2,-4)

C

`(-9//8,9//2)`

D

(2,4)

Text Solution

Verified by Experts

The correct Answer is:
A
We have,
`y^(2)=18x`
`rArr" "2y(dy)/dt=18(dx)/(dt)`
`rArr" " 2yxx2(dx)/(dt)=18(dx)/(dt)" "[:'(dy)/(dt)=2(dx)/(dt)]`
`rArr" "2y=18 rArr y=9/2`
When `y=9/2`, we have
`(9/2)^(2) = 18x rArr x =9/8`
Hence, the required point is `(9//8,9//2)`
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