Question
Mathematics Question on Circle
If the circle
x2+y2-2gx+6y-19c = 0,g,c∈R
passes through the point (6, 1) and its centre lies on the line x – 2 cy = 8, then the length of intercept made by the circle on x -axis is
A
√11
B
4
C
3
D
2√23
Answer
2√23
Explanation
Solution
The correct answer is (D):
Circle : x 2 + y 2 – 2 g x _ + _6 y – 19 c = 0
It passes through h(6, 1)
⇒ 36 + 1 – 12 g + 6 – 19 c = 0
= 12 g + 19 _c = _43 …(1)
Line x – 2 cy = 8 passes though centre
⇒ g + 6 c = 8 …(2)
From (1) & (2)
_g = _2, c = 1
C : x 2 + y 2 – 4 x + 6 y – 19 = 0
x\int = 2√g2-C
= 24+19
=223