Question

The abscissa of A and B are the roots of the equation

x² + 2ax – b² = 0 and their ordinates are the roots of the equation y² + 2py – q² = 0. The equation of the circle with AB as diameter:

• A. x² + y² + 2ax + 2py – b² – q² = 0
• B. x² + y² + 2ax + py – b² – q² = 0
• C. x² + y² + 2ax + 2py + b² + q² = 0
• D. None of these

Answer 1

Answer: (A)

x² + y² + 2ax + 2py – b² – q² = 0

Answer 2

Let A ŗ (x₁, y₁) and B ŗ (x₂, y₂)

Q x₁, x₂ are roots of x² + 2ax – b² = 0

Ž (x – x₁) (x – x₂) = x² + 2ax – b²

Q y₁, y₂ are roots of y² + 2py – q² = 0

Ž (y – y₁) (y – y₂) = y² + 2py – q²

Now equation of circle with AB as diameter is

(x – x₁) (x – x₂) + (y – y₁) (y – y₂) = 0

Ž x² + 2ax – b² + y² + 2py – q² = 0

Ž x² + y² + 2ax + 2py – b² – q² = 0