The slope of the tangent to a curve at any point (x, y) on the curve is -x/y . Find the equation of the curve if the point (3,-4) on the curve.

Answer 1

you might have noticed that if we find dy/dx for a circle of the form x^2 + y^2 = r^2 we get
2x + 2y dy/dx = 0
dy/dx = -2x/(2y) = -x/y

So we had a circle of the form x^2 + y^2 = r^2
plug in the given point to find r^2
and you are done.