Question
Question: A diameter of x<sup>2</sup> + y<sup>2</sup> –2x –6y + 6 = 0 is a chord to circle centre (2, 1), then...
A diameter of x2 + y2 –2x –6y + 6 = 0 is a chord to circle centre (2, 1), then radius of the circle
A
1
B
2
C
3
D
4
Answer
3
Explanation
Solution
Given S1 = x2 + y2 –2x – 6y + 6 = 0
and S2 = (x –2)2 + (y –1)2 = r2
ή common chord = S1 – S2 = 0
= 2x – 4y + (1 + r2) = 0
This chord being dia of S1 so passes through centre (1, 3) of S1
ή 2 – 12 + 1 + r2 = 0 ή r = ± 3 only (+ve) ή r = 3