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 (x−h)2+(y−k)2=k2⇒x2 + y2−2hx−2ky+h2 = 0 Length of the intercept on y-axis is 2l ⇒ 2√k2−h2 = 2l ⇒k2−h2=l2 Locus of (h, k) is y2 - x2 = l2