The slope of the tangent to a curve at any point (x, y) on the curve is x divided by y . Find the equation of the curve if the point (2, -3) is on the curve.

Question

A) x2 + y2 = 13

B) x2 + y2 = 25

C) x2 - y2 = -5

D) x2 - y2 = 5

Answer 1

The answer is c, since the slope of the tangent line to a curve is dY/dX, so:

dY / dX = X / Y which is given. Now cross multiply:

Y dY = X dX Multiply both sides by 2:

2Y dY - 2X dX Now get integral from both sides:

Y^2 = X^2 + C Now plug the given point (2, -3) to get the C.

9 = 4 + C

C = 5 so:

Y^2 = X^2 + 5 Now move y^2 to the right and 5 to the left, so:

X^2 - Y^2 = -5 Which is the letter c.