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

Answer 1

the slope is \(\frac{x}{y}\)?

Answer 2

yes

Answer 3

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

Answer 4

That's what i'm thinking

Answer 5

in other words this is the unit circle

Answer 6

I guess so

Answer 7

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

Answer 8

this one is "separable"

Answer 9

y ' = x/y

dy/dx = x/y

y*dy = x*dx

integrate both sides to get

(y^2)/2 = (x^2)/2 + C

Answer 10

hopefully you see what to do from here

Answer 11

Ohh I think i see know. Give me a second

Answer 12

are you able to determine the value of C?