Question

Show that the curve x = 6 cos(t), y = 5 sin(t) cos(t) has two tangents at (0, 0) and find their equations.

Answer 1

We can write
  cos(t) = x/6
so
  y = 5(±√(1 -(x/6)^2)*x/6
Then
  y' = (±5/6)*(√(1 -(x/6)^2) + x/(2√(1 -(x/6)^2)*(-2(x/6))
The limit as x → 0 is ±5/6

The equations of the two tangents are
  y = (5/6)x
  y = (-5/6)x