If y + 3x = 0 is the equation of a chord of the circle x^2+y^2-30x = 0, then the equation of the circle with this chord as diameter is:

JEE Main 2015 Mathematics question

If is the equation of a chord of the circle , then the equation of the circle with this chord as diameter is:

(1)
(2)Correct
(3)
(4)

Answer: (2)

Solution

Any circle through the points where the line meets the given circle belongs to the family , i.e. . Its centre is . For the chord to be a *diameter* of this new circle, its centre must lie on the chord $3x

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Question ID VK-115293