The equation of the tangent at (3cosθ , 2sinθ) on
x2
9
+
y2
4
= 1 is
x
3
cosθ +
y
2
sinθ = 1 ..... (i) The equation of director circle is x2+y2 = 9 + 4 = 13 ..... (ii) The combined equation of CP and CQ is obtained by homogenizing equation (ii) with (i). Thus combined equation is x2+y2 = 13 (
x
3
cosθ+
y
2
sinθ)2 ⇒ (
13
9
cos2θ−1)x2 +
13
3
sinθ cosθ xy + (
13
4
sin2θ−1)y2 = 0 ∴ Product of the slopes of CP and CQ =
