Question

The abcissa and ordinate of the end points A and B of a focal chord of the parabola y² = 4x are respectively the roots of x² – 3x + a = 0 and y² + 6y + b = 0. The equation of the circle with AB as diameter is.

• A. x² + y² – 3x + 6y + 3 = 0
• B. x² + y² – 3x + 6y – 3 = 0
• C. x² + y² + 3x + 6y – 3 = 0
• D. x² + y² – 3x – 6y – 3 = 0

Answer 1

Answer: (B)

x² + y² – 3x + 6y – 3 = 0

Answer 2

t₁ t₂ = – 1 as AB is focal chord

x² – 3x + a = 0 ; x₁ + x₂ = 3 & x₁x₂ = a

y² + 6y + b = 0 ; y₁ + y₂ = – 6 & y₁y₂ = b

x₁x₂ = $\frac{1}{t_{1}^{2}}$. t₁² = 1 = a

y₁y₂ = 2t₁$\left( - \frac{2}{t_{1}} \right)$ = – 4 = b

a = 1, b = – 4

equation of circle AB is diameter

x² + y² – 3x + 6y – 3 = 0