Question

Question #92d58

Answer 1

y = m x represents the family of straight lines through the origin. Every member of the family has a specific value for the parameter m.
Its differential equation is `x dy/dx - y = 0`/

Explanation:

Differentiate with res[ect to x and eliminate the parameter m = `y/x`.

The family of circles with center at (m, n) and radius a is given by
`( x - m )^2 + ( y - n )^2 = a^2`.

For the family of equal circles with fixed radius a, m and n are parameters of the family. We have to differentiate twice in succession and eliminate both m and n, using the given equation as the third for the purpose.