Differential Equation Family of Curves

Question

Find the Differential Equation of the family of plane curves:

Straight lines tangent to the circle x^2+y^2=4

Straight lines tangent to a parabola y=4x^2

Answer 1

Lawrence:

Use implicit differentiation for first part:

2*x + 2*y*(dy/dx) = 0

Then 2*y*(dy/dx) = - 2*x

(dy/dx) = (-2x)/(2y) = -x/y