The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y. What is the equation of the curve if (2, 1) is a point on the curve?

Answer 1

dy/dx = x/y
y dy = x dx
y^2 = x^2 + c
using the point (2,1)
1 = 4+c
c = -3

x^2-y^2 = 3