JEE MAIN - Mathematics (2004 - No. 32)
A point on the parabola $${y^2} = 18x$$ at which the ordinate increases at twice the rate of the abscissa is
$$\left( {{9 \over 8},{9 \over 2}} \right)$$
$$(2, -4)$$
$$\left( {{-9 \over 8},{9 \over 2}} \right)$$
$$(2, 4)$$
ব্যাখ্যা
$${y^2} = 18x \Rightarrow 2y{{dy} \over {dx}} = 18 \Rightarrow {{dy} \over {dx}} = {9 \over y}$$
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 $$\left( {{9 \over 8},{9 \over 2}} \right)$$
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 $$\left( {{9 \over 8},{9 \over 2}} \right)$$