Question

Find the orthogonal trajectories of the family of curves. (Use C for any needed constant.)
x^2 + 2y^2 = 14k^2

Help understanding and working out. Tried solving for dy/dx and than putting that under -1 resulting in 2y/x but that didn't result in the correct solution...

Answer 1

replace dy/dx by -dx/dy and then u can derive the result

Answer 2

is the ans x2=cy

Answer 3

Isn't that the same as -1/(dy/dx)?
B/c I took the derivative across the whole equation and got 2x+4y (yd/dx) = 0 then I solved for dy/dx and got 2x/-4y. so for the answer as to the orthoginals I thought id be... -1/(2x/4y)

Answer 4

Okay, so that should be... 2y/x again... am I supposed to integrate this or something?

Answer 5

u should integrate back

Answer 6

Wow, kinda silly that I didn't remember that...

Answer 7

sometimes it happens

Answer 8

Uck... it's still wrong though... -_-

Answer 9

is it y=cx^2

Answer 10

How did you get that though?

Answer 11

arrange for constant

Answer 12

What?

Answer 13

So, solve for y first?