A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is

Question

A point on the parabola y2 = 18x at which the ordinate increases at twice the rate of the abscissa is (A) (2, 4) (B) (2, -4) (C) ((-9/8), (9/2)) (D) ((9/8), (9/2))

Tardigrade Admin · Accepted Answer

Any point be ( (9/2) t2, 9t ) ; differentiating y2 = 18x ⇒ (dy/dx) = (9/y) = (1/t) = 2 (given) ⇒ t = (1/2) ⇒ Point is ((9/8), (9/2))

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

$(2, 4)$

$(2, - 4)$

$(\frac{- 9}{8}, \frac{9}{2})$

$(\frac{9}{8}, \frac{9}{2})$

Any point be $(\frac{9}{2} t^{2}, 9 t);$ differentiating $y^{2} = 18 x$
$\Rightarrow \frac{d y}{d x} = \frac{9}{y} = \frac{1}{t} = 2$ (given) $\Rightarrow t = \frac{1}{2}$
$\Rightarrow$ Point is $(\frac{9}{8}, \frac{9}{2})$

Q. A point on the parabola y2=18x at which the ordinate increases at twice the rate of the abscissa is

(2,4)

(2,−4)

(8−9​,29​)

(89​,29​)