Question

The extremities of a diagonal of a rectangle are (0, 0) and (4, 4). The locus of the extremities of the other diagonal is x² + y² – λ₁ x – λ₂ y= 0, then (λ₁ + λ₂ ) equals

(A) 0 

(B) 8 

(C) – 8 

(D) 16

Answer 1

Correct Answer is: (B) 8 

The locus of the extremities of the other diagonal is the circle with given diagonal as diameter.

⇒ (x – 0) (x – 4) + (y – 4) (y – 0) = 0

⇒ x² + y² – 4x – 4y = 0

Aliter: (AE)² = (DE)²

(h – 2)² + (k – 2)² = (2√2)²

∴ x² + y² – 4x – 4y = 0.