The slope of the tangent line to a curve at any point (x, y) on the curve is x divided by y . What is the equation of the curve if (4, 1) is a point on the curve?

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

A	x2 - y2 = 15
B	x2 + y2 = 15
C	x + y = 15
D	xy = 15

Answer 1

plug the point into each equation, only A is correct, 4^2 - 1^2 = 15

take the derivative of x^2 - y^2 = 15 to get 2x -2yy' = 0, solve for y'

2yy' =2x

y' = x/y

the derivative = slope