Question

The slope of the tangent line to a curve at any point (x, y) on the curve is x/y. What is the equation of the curve if (4, 1) is a point on the curve?

a) x^2-y^2=15
b) x^2+y^2=15
c) x+y=15
d) xy=15

Answer 1

Well, if (4,1) lies on the curve, then it must satisfy the given equations.

It only satisfies a) x^2 - y^2 = 15

Just to make sure ...
2x - 2y dy/dx = 0
dy/dx = 2x/2y = x/y

Yup, it is a)