A point on the parabola y^2 = 18x at which the ordinate increases at twice the rate of the…

Question

A point on the parabola ${y^2} = 18x$ at which the ordinate increases at twice the rate of the abscissa is

Accepted Answer

$${y^2} = 18x \Rightarrow 2y{{dy} \over {dx}} = 18 \Rightarrow {{dy} \over {dx}} = {9 \over y}$$

Given $${{dy} \over {dx}} = 2 \Rightarrow {9 \over 2} = 2 \Rightarrow y = {9 \over 2}$$

Puting in $${y^2} = 18x \Rightarrow x = {9 \over 8}$$

$$\therefore$$ Required point is $$\left( {{9 \over 8},{9 \over 2}} \right)$$

Solutions · 1