Question

The equation of the chord of contact of a point P(x₁, y₁) with respect to the circle S = 0 is s₁ = 0.

Answer 1

Let (bar)AB be the chord of contact of P (see Fig.). Suppose A = (x₂, y₂) and B = (x₃, y₃). The equation of the tangent at A(x₂, y₂) is S₂ = 0.

This tangent passes through (x₁ ,y₁) ⇒ S₂₁ = S₁₂ Therefore, the point A(x₂, y₂) satisfies the first-degree equation S₁ = 0. Similarly, S₁₃ = 0 implies that the point B(x₃, y₃) satisfies the firstdegree equation S₁ = 0. Hence, the equation of the chord (bar)AB is S₁ = 0.