Use the method described in to show that the orthogonal trajectories to the family of curves x2 + y2 = kx, k a parameter, satisfy Find the orthogonal trajectories by solving the above equation. Sketch the family of curves, along with their orthogonal trajectories. [Hint: Try multiplying the equation by xmyn as in 30.]

Solution:Step 1In this problem we have to show that the orthogonal trajectories to the family of curves , k a parameter satisfy .