CircleEasy
Question
The equation of a circle touching the parabola y = x2 at the point (1, 1) and passing through the point (2, 2) is :-
Options
A.x2 + y2 - 6x + 4 = 0
B.x2 + y2 - 6y + 4 = 0
C.x2 + y2 + 6x + 4 = 0
D.x2 + y2 + 6y + 4 = 0
Solution
Eq. of tangent to parabola y = x2 at P(1, 1) is
2x - y - 1 = 0
Eq. of circle is
(x - 1)2 + (y - 1)2 + λ(2x - y -1) = 0 ....(i)
Circle passes through Q(2, 2)
∴ (2 - 1)2 + (2 - 1)2 + λ(4 - 2 - 1) = 0
⇒ λ = - 2
Put λ = - 2 in (i)
x2 + y2 - 6x + 4 = 0
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