Question

If tangents at points (x₁, y₁) and (x₂, y₂) of circle x² + y² + 2gx + 2fy + c = 0 are perpendicular to each other than prove that x₁x₂ + y₁y₂ + g(x₁ + x₂) + f(y₁ + y₂) + g² + f² = 0

Answer 1

Given equation of circle

x² + y² + 2gx + 2fy + c = 0 …..(i)

Equation of tangent at point (x₁, y₁)

xx₁ + yy₁ + g(x + x₁) +f(y + y₁) + c = o

⇒ x₆x + y₆y + g(x₁ + x) +f(y₁ + y) + c = 0 …..(ii)