Question

Find the equation of the normal at P of the circle S = 0 where P and S are given by P = (3, –4), S ≡ x² + y² + x + y – 24.

Answer 1

Equation of the normal is

(x – x₁) (y₁ + f) – (y – y₁) (x₁ + g) = 0 

(x – 3) (– 4 + 1/2) – (y + 4) (3 + 1/2) = 0 

– 7/2 (x –3) – 7/2 (y + 4) = 0 

⇒ (x – 3) + (y + 4) = 0 

x – 3 + y + 4 = 0 

x + y + 1 = 0