ParabolaHard

Question

The centre of the circle passing through the point (0, 1) and touching the curve y = x2 at (2, 4) is

Options

A.
B.
C.
D.None of these

Solution

     
Let centre of circle be (h, k).
So that,       OA2 = OB2
⇒     h2 + (k -1)2 = (h - 2)2 + (k - 4)2
⇒     4h + 6k - 19 = 0       .....(i)
Also, slope of OA and slope of tangent at (2, 4) to y = x2 is 4.
And (slope of OA). (slope of tangent at A) = - 1
∴     . 4 = - 1
⇒     4k - 16 = - h + 2
      h + 4k = 18         ....(ii)
On solving Eqs. (i) and (ii), we get
    and
∴ Centre coordinates aare ,

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