Vikas TU
Last Activity: 8 Years ago
The parametric equations define the circle of radius a, centered on the origin. When you refer to parametric angles of the tangents, I will suppose you mean the parameters corresponding to their points of tangency.
Let P and Q be the moving points of tangency, where angle POQ = 60°.
Let R be the intersection of the tangents. You are looking for the locus of R.
angle OPR = angle OQR = 90°
That makes OPRQ a cyclic quadrilateral, so angle PRQ = 120°, as opposite angles are supplementary.
By symmetry OR must bisect angles POQ and PRQ.
Therefore, angle ROP = 30°, and ∆RPO is a right triangle.
OR = 2OP = 2a/√(3)
The locus of R is the circle with radius 2a/√(3), centered on the origin
