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

Answer

D

Explanation

Given `y^(2)=18x`
`implies2y. (dy)/(dt)=18 (dx)/(dt)`
Given `(dy)/(dx)=2(dx)/(dt)`
`:.2y.2=18`
`impliesy=9/2`
From Eq (i) `(9/2)^(2)=18x`
`impliesx=81/(4xx18)`
`impliesx=9/8`
`:.` Required point is `(9/8,9/2)`.