Question
Question: A triangle is formed by the lines whose combined equation given by (x + y – 4) (xy – 2x – y + 2) = 0...
A triangle is formed by the lines whose combined equation given by (x + y – 4) (xy – 2x – y + 2) = 0. The equation of circumcircle is –
A
x2 + y2 – 5x – 3y + 8
B
x2 + y2 – 3x – 5y + 8 = 0
C
x2 + y2 – 3x – 5y – 8 = 0
D
None of these
Answer
x2 + y2 – 3x – 5y + 8 = 0
Explanation
Solution
(x + y – 4) (xy – 2x – y + 2) = 0
x + y – 4 = 0, x(y – 2) – 1(y – 2) = 0
(y – 2) (x – 1) = 0
y – 2 = 0
x = 1
equation of circumcircle
(x –1)(x – 2) + (y – 2)(y – 3) = 0
x2 – 3x + 2 + y2 – 5y + 6 = 0
x2 + y2 – 3x – 5y + 8 = 0