If a circle passing through the point (-1,0) touches y-axis at (0,2), then the x-intercept of the circle is

JEE Main 2015 Mathematics question

If a circle passing through the point touches -axis at , then the -intercept of the circle is

(1)
(2)5
(3)
(4)3Correct

Answer: (4)

Solution

Since the circle touches the -axis at , the radius to that point is horizontal, so the centre is and the radius equals . The circle also passes through , so

(-1- + (0- = ⇒ 1 + 2h + + 4 = ⇒ 2h = -5,

giving . The circle is $

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Question ID VK-115384