Question

Find the family of ortogonal curves from the family: y^2=4(x-a)

Answer 1

Please help me it's for a test. The answer options are:
a) y=be^(x/2)
b) y=be^(-x)
c) y=be^(-x/2)

Answer 2

first differentiate implicitly:
2yy'=4
for the orthogonal curve the slope will be -1/y'. Put this value in the equation:
2y(-1/y')=4
separate variables and solve for y:
y'/y=1/2 or dy/y=-dx/2
Ln|y|=-x/2 + C or y= e^(-x/2 +C)=e^(-x/2)*e^b=e^(-x/2)*b
so answer a)

Answer 3

sry, :) c)

Answer 4

Thanks :)

Answer 5

you wellcome