Question

Find the point on the curve y^2=8x for which the abscissa and ordinate change at the same rate.

Answer 1

According to question,
Rate of change of Abscissa = rate of change of ordinate
⇒dx = dy ---------(1)

equation , y² = 8x
differentiate with respect to x
2y.dy/dx = 8
2ydy = 8dx
from equation (1)
2y = 8 ⇒ y = 4 , now put it in equation of curve
y² = 8x
⇒(4)² = 8x
⇒ 16 = 8x ⇒ x = 2

Hence, point on the curve is (2,4)