Question
Question: If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10p...
If the lines 2x + 3y + 1 = 0 and 3x – y – 4 = 0 lie along diameters of a circle of circumference 10p, then the equation of the circle is-
A
x2 + y2 – 2x + 2y – 23 = 0
B
x2 + y2 – 2x – 2y – 23 = 0
C
x2 + y2 + 2x + 2y – 23 = 0
D
x2 + y2 + 2x – 2y – 23 = 0
Answer
x2 + y2 – 2x + 2y – 23 = 0
Explanation
Solution
Solving 2x + 3y + 1 = 0 and 3x – y –4 = 0
we get centre (1, –1)
As circumference = 10p
2pr = 10p ή r = 5
required equation of circle is
(x – 1)2 + (y + 1)2 = 52