I need help please!

Question

The slope of the tangent line to a curve at any point (x, y) on the curve is . What is the equation of the curve if (3, 1) is a point on the curve?

Options:

1)	x2 + y2 = 8
2)	x + y = 8
3)	x2 - y2 = 8
4)	xy = 8

Answer 1

We have dy/dx = x/y, we separate variables xdx = ydy. Integration of both sides: ∫xdx = ∫ydy or x²/2 = y²/2 + C/2; x² - y² = C; Point (3,1) on this curve, so 3² - 1² = C, or C = 8.

Answer: x² - y² = 8 or version 3).