Answer:
y = Ax^2
Step-by-step explanation:
below is the detailed solution
To determine the orthogonal trajectories of the family of curves
X^2 + 2y^2 = 17k^2
we have to differentiateX^2 + 2y^2 = 17k^2 with respect to x
= 2x + 4y dy/dx = 0
Hence : dy/dx = - x/2y
we have to determine the negative reciprocal
dy/dx = 2y/x ----------- 1
integrate equation 1
∫dy/2y = ∫dx/x
= 1/2 log y = log x + log c
log y = 2logx + 2logc
log y = logx^2 + logC^2
therefore : y = Ax^2 ; where C^2 = A
