Choose the correct or the most suitable answer from the given four alt

1.	Choose the correct or the most suitable answer from the given four alternatives.The equation of the circle passing through (1,5) and (4, 1) and touching y-axis is x2 + y2 – 5x – 6y + 9 + λ(4x + 3y – 19) = 0 where λ is equal to … (a) 0, -40/9(b) 0 (c) 40/9(d) -40/9
Answer» (a) 0, -40/9 x² + y² – 5x – 6y + 9 + λ(4x + 3y -19) = 0 ie., x² + y² + x(4λ – 5) + y(3λ – 6) + 9 — 19λ = 0 Since it touches y axis x = 0 ⇒ y² + y(3λ – 6) + 9 – 19λ = 0 It is a quadratic in y, Since the circle touches y axis the roots must be equal ⇒ b² – 4ac = 0 ie.,(3λ – 6)² – 4(1) (9 – 19λ) = 0 Solving we get λ = o or -40/9

Choose the correct or the most suitable answer from the given four alternatives.The equation of the circle passing through (1,5) and (4, 1) and touching y-axis is x2 + y2 – 5x – 6y + 9 + λ(4x + 3y – 19) = 0 where λ is equal to … (a) 0, -40/9(b) 0 (c) 40/9(d) -40/9

Answer»

(a) 0, -40/9

x² + y² – 5x – 6y + 9 + λ(4x + 3y -19) = 0

ie., x² + y² + x(4λ – 5) + y(3λ – 6) + 9 — 19λ = 0

Since it touches y axis x = 0

⇒ y² + y(3λ – 6) + 9 – 19λ = 0

It is a quadratic in y,

Since the circle touches y axis the roots must be equal

⇒ b² – 4ac = 0

ie.,(3λ – 6)² – 4(1) (9 – 19λ) = 0

Solving we get λ = o or -40/9