JEE Advanced 2010 Mathematics question

Let A and B be two distinct points on the parabola . If the axis of the parabola touches a circle of radius r having AB as its diameter, then the slope of the line joining A and B can be

(A)
(B)
(C)Correct
(D)Correct

Answer: (C),(D)

Solution

Let and with . The centre of the circle on AB as diameter is the mid-point . The axis of the parabola is the x-axis (); it touches the circle when the distance of the centre from the x-axis equals the radius:

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Question ID VK-025770