(a)
Equation of the circle is (x – x1) (x – x2) + (y – y1) (y – y2) = 0
i.e., (x + 5) (x – 1) + (y – 1) (y – 3) = 0
⇒ x2 + 5x – x – 5 + y2 – 3y – y + 3 = 0
⇒ x2 + y2 + 4x – 4y – 2 = 0.
Equation of the circle is (x – x1)(x – x2) + (y – y1) (y – y2) = 0
i.e., (x – 2)(x – 0) + (y – 0) (y – 2) = 0
x2 – 2x + y2 – 2y = 0
⇒ x2 + y2 – 2x – 2y = 0
(c) Given A(3,4) B(1, -2)
∴ Required equation is (x – x1)(x – x2) + (y – y1) (y – y2) = 0
i.e., (x – 3) (x – 1) + (y – 4) (y + 2) = 0
x2 – x – 3x + 3 + y2 + 2y – 4y – 8 = 0
⇒ x2 + y2 – 4x – 2y – 5 = 0.
