Question
Question: Equation of circle passing through the point of intersection of circles x<sup>2</sup> + y<sup>2</sup...
Equation of circle passing through the point of intersection of circles x2 + y2 = 6 and x2 + y2 – 6x + 8 = 0 and point (1, 1) is-
A
x2 + y2 – 6x + 4 = 0
B
x2 + y2 – 3x + 1 = 0
C
x2 + y2 – 4y + 2 = 0
D
x2 + y2 – 6x – 6y + 10 = 0
Answer
x2 + y2 – 3x + 1 = 0
Explanation
Solution
S ŗ x2 + y2 – 6 = 0
S¢ = x2 + y2 – 6x + 8 = 0
Required circle
S + lS¢ = 0
x2 + y2 – 6 + l(x2 + y2 – 6x + 8) = 0 …….(1)
Q (1) passes through (1, 1)
1 + 1 – 6 + l(1 + 1 – 6 + 8) = 0
Ž l = 1
Put in (1) to get circle
x2 + y2 – 3x + 1 = 0