A curve in the first quadrant is such that the slope of O P is twice the slope of the tangent drawn at P to the curve, where O is the origin and P is any general point on the curve. If the curve passes through 4 , 2 , then its equation is

Question

A curve in the first quadrant is such that the slope of O P is twice the slope of the tangent drawn at P to the curve, where O is the origin and P is any general point on the curve. If the curve passes through 4 , 2 , then its equation is, y = x 2 - 14, y 2 = x, y = x 3 - 62, y = sin ⁡ x - 4 + 2

MARKS App · Accepted Answer

Slope of O P = 2 d y d x P ⇒ y x = 2 d y d x ⇒ 2 ∫ d y y = ∫ d x x ⇒ 2 ln ⁡ y = ln ⁡ x + ln ⁡ c ⇒ y 2 = c x As it passes through 4 , 2 ⇒ c = 1 ∴ the equation of the curve is y 2 = x

Search any question & find its solution

Looking for more such questions to practice?