Question

Find the orthogonal trajectories of the family of curves.
x^2 + 2y^2 = k^2

Answer 1

first find dy/dx yes?

Answer 2

im not sure if my dy/dx is correct.

Answer 3

i got

Answer 4

that's right. So what is the slope that is perpendicular to that?

Answer 5

its 2y/x

Answer 6

so dy/dx = 2y/x yes?

Answer 7

then i seperated the x and y's and got dy/2y = dx/x

Answer 8

ok, integrate then what do you get?

Answer 9

i got (1/2)ln(y) = 2(ln(x)) + C

Answer 10

not sure if thats right haha.

Answer 11

should be (1/2) lny = lnx + C

Answer 12

oh yeah, i just simplified the y so i got 2(lnx + c)

Answer 13

then y = Ce^(2lnx)

Answer 14

but the book answer is different from this.

Answer 15

simplify further

Answer 16

e^2lnx = 2?

Answer 17

OHHH

Answer 18

2LN X turns into lnx^2