Question

A family of curves forms orthogonal trajectories with another family of curves if each curve in one family is perpendicular to each curve in the other family at each point of intersection. Use implicit differentiation if needed to find dy/dx for each equation of the following pairs.
y=mx ; x^2+y^2=a^2 where m and a are constants.

Find dy/dx for y=mx in terms of of x and y only.

Answer 1

if y=mx, what is y'?

Answer 2

if m is a constant, wouldn't it just be x

Answer 3

no, y = mx, solve for m

Answer 4

m=y/x

Answer 5

correct

Answer 6

take the derivative of that?

Answer 7

so, y' = m, or rather y' = y/x

Answer 8

I don't have to take the derivative of y/x ?

Answer 9

no, as far as i can read ... you define y' in terms of y and x only

Answer 10

if y=mx, then y' = m .... which is just y/x

Answer 11

oh you're right thanks

Answer 12

youre welcome