The slope of the tangent to a curve at any point (x, y) on the curve is negative 1 times x divided by y . Find the equation of the curve if the point (2, -2) is on the curve.

Question

A)x + y = 0

B)x² - y² = -2

C)x² + y² = 16

D)x² + y² = 8

I believe the answer is D

Answer 1

dy/dx = - x/y; ydy = - xdx. We integrate both sides: ∫ydy = - ∫x²dx; y²/2 = - x²/2 + C/2; x² + y² = C Using point

(2, -2) we have 4 + 4 = C; C = 8;

So, x² + y² = 8

Answer is D)