Let any fixed point P be (h, k)

equation of tangent at P (h, k) to the ellipse is

……(1)

Let any point Q ( α α , β β ) be on tangent represented by equation (1)

⇒ ⇒

⇒ ⇒ ……(2)

Now chord of contact of ellipse w.r.t. Q ( α α , β β ) is

⇒ ⇒ (from equation (2))

⇒ ⇒ ……(3)

Clearly equation (3) represents a family of lines passes through a fixed point and coordinate of that fixed point is given by M .

Now, slope of OM, M OM = and slope of OP, M OP =

⇒ ⇒ M OM × × M OP = × × = .

Clearly M OM × × M OP ≠ ≠ –1 ⇒ ⇒ the line PM never subtends right angle at origin.

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