Question

The slope of a curve at any point is the reciprocal of twice the ordinate of the point. The curve also passes through the point (4, 3). Find the equation of the curve.

Answer 1

Slope at any point (x, y) is the slope of the tangent at (x, y)

dy/dx = 1/2y

⇒ 2y dy = dx

⇒ ∫2y dy = ∫dx + c 

⇒ y² = x + c 

Since the curve passes through (4, 3) 

we have 9 = 4 + c ⇒ c = 5 

Equation of the curve is y² = x + 5