Question

Find the points on the parabola y²=4x for which the rate of change of abscissa and coordinate is same.

Answer 1

we have to find the points on the parabola, y² = 4x for which the rate of change of abscissa and coordinate is same.

i.e., dx/dt = dy/dt ......(1)

now , y² = 4x

differentiating both sides with respect to time,

2ydy/dt = d(4x)/dt = 4 (dx/dt)

⇒y(dy/dt) = 2 (dx/dt) ......(2)

from equations (1) and (2),

y(dy/dt) = 2(dy/dt)

⇒y = 2

putting y = 2 in equation, y² = 4x

(2)² = 4x ⇒x = 1

hence, (1, 2) is the point on the curve y² = 4x, for which the rate of change of abscissa and coordinate is same.