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

Options

A. `(9//8,9//2)`
B. (2,-4)
C. `(-9//8,9//2)`
D. (2,4)

Answer

A

Explanation

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)`