If the line x + 2ky + 3 = 0 is a diameter of the circle x2 + y2 – 6x + 2y = 0, then k is equal to
(a) 3
(b) -5
(c) -1
(d) 5
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If the line x + 2ky + 3 = 0 is a diameter of the circle x2 + y2 – 6x + 2y = 0, then k is equal to
(a) 3
(b) -5
(c) -1
(d) 5
If the line x + 2ky + 3 = 0 is a diameter of the circle x2 + y2 – 6x + 2y = 0, then k is equal to
(a) 3
(b) -5
(c) -1
(d) 5
Correct option: (a) 3
Explanation:
Given,
Equation of Circle: x2 + y2 – 6x + 2y = 0
x2 + y2 – 6x + 2y = 0
=> (x – 3)2 + (y + 1)2 = 10
From the above equation,
Centre: (3, -1)
Radius: √10
Since centre lies on the diameter so,
(3, -1) will lie on the diameter x + 2ky + 3 = 0
=> 3 – 2k + 3 = 0
=> 6 – 2k =0
=> k = 3