If (a, b) and (-5, 1) are the two end points of diameter of the circle

1.	If (a, b) and (-5, 1) are the two end points of diameter of the circle x2 + y2 + 4x – 4y = 2. Find the value of a and b.
Answer» Given (x_1, y₁) = (a, b) (x₂, y₂) = (-5, 1) & Center of the given circle = (-2, 2). Equation of the circle when ends of diameter is given is (x – x₁) (x – x₂) + (y – y₁) (y – y₂) = 0. (x – a) (x + 5) + (y – b) (y – 1) = 0. ⇒ x² – 5a – ax + 5x + y² – by – y + b = 0. x² + y² + x (5 – a) – y(b + 1) + (b – 5a) = 0 comparing. This by given circle x² + y³+ 4x – 4y – 2 = 0 we get 5 – a = 4, b + 1 = 4 ⇒ 5 – 4 = a, b = 4 – 1 ∴ a = 1 & b = 3.

If (a, b) and (-5, 1) are the two end points of diameter of the circle x2 + y2 + 4x – 4y = 2. Find the value of a and b.

Answer»

Given (x_1, y₁) = (a, b) (x₂, y₂) = (-5, 1) & Center of the given circle = (-2, 2).

Equation of the circle when ends of diameter is given is (x – x₁) (x – x₂) + (y – y₁) (y – y₂) = 0.

(x – a) (x + 5) + (y – b) (y – 1) = 0.

⇒ x² – 5a – ax + 5x + y² – by – y + b = 0.

x² + y² + x (5 – a) – y(b + 1) + (b – 5a) = 0 comparing.

This by given circle x² + y³+ 4x – 4y – 2 = 0

we get 5 – a = 4, b + 1 = 4

⇒ 5 – 4 = a, b = 4 – 1

∴ a = 1 & b = 3.

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If (a, b) and (-5, 1) are the two end points of diameter of the circle x2 + y2 + 4x – 4y = 2. Find the value of a and b.

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