ParabolaMedium
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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