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Question

A circle touches x-axis and cuts off a constant length 2l from the y-axis. The locus of its centre is

A
+ =
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B
+ = 2
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C
+ = 3
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D
+ =
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Solution

The correct option is D + =
Let C(h, k) be the centre of the circle
Circle touches x-axis radius = |k|
Equation of the circle with centre (h, k) and radius |k| is
(xh)2+(yk)2=k2 x2 + y22hx2ky+h2 = 0
Length of the intercept on y-axis is 2l 2k2h2 = 2l k2h2=l2
Locus of (h, k) is y2 - x2 = l2

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