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 (3, 1) is a point on the curve?

Question

anonymous · Answer

the slope is $\frac{x}{y}$?

anonymous · Answer

yes

anonymous · Answer

i think that means $$y'=\frac{x}{y}$$ right?

anonymous · Answer

That's what i'm thinking

anonymous · Answer

in other words this is the unit circle

anonymous · Answer

I guess so

anonymous · Answer

ah dang i am wrong, if it was the unit circle then it would be 
$$y'=-\frac{x}{y}$$

anonymous · Answer

this one is "separable"

jim_thompson5910 · Answer

y ' = x/y

dy/dx = x/y

y*dy = x*dx

integrate both sides to get

(y^2)/2 = (x^2)/2 + C

jim_thompson5910 · Answer

hopefully you see what to do from here

anonymous · Answer

Ohh I think i see know. Give me a second

jim_thompson5910 · Answer

are you able to determine the value of C?