A circle passes through the point (0,1) and touches the parabola y = x^ 2 at the point (1,1). The centre of the circle is...

MHT CET 2026 Mathematics question

A circle passes through the point (0,1) and touches the parabola at the point (1,1). The centre of the circle is...

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

Answer: (C)

Solution

Let the centre be . The circle passes through and , so the centre is equidistant from them: . The circle touches the parabola at , so the radius to is along the normal to the parabola there. The slope of the tangent is

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Question ID VK-100907