Question

The slope of the tangent to a curve at a point P(x, y) is 2y/x, x, y > 0 and which passes through the point (1, 1), find the equation of the curve.

Answer 1

Given condition is

dy/dx = 2y/x

dy/y = 2.dx/x

Integrating, we get 

log |y| = 2log |x| + log |c| 

y = cx²

which is passing through the curve (1, 1), so c = 1 

Hence, the equation of the curve is 

y = x²