Practicing Success
The point on the curve $y^2=8 x$ for which the abscissa and ordinate change at the same rate is : |
(2, 4) (4, 2) (0, 2) (2, 0) |
(2, 4) |
$y^2=8 x$ .......(1) differentiating a function on both sides w.r.t to a variable t $\frac{d}{d t}\left(y^2\right)=\frac{d}{d t}(8 x)$ $= 2 y \frac{d y}{d t}=8 \frac{d x}{d t}$ .......(2) for all rate of change of x and y let $\frac{d y}{d t}=\frac{d x}{d t}=k$ So eq. (2) is 2yk = 8k ⇒ 2y = 8 ⇒ y = 4 from (1) extracting value of x so (4)2 = 8x x = 16/8 x = 2 So (x, y) = (2, 4) → same rate of charge of both variables |