Maths-
General
Easy
Question
The P be the family of parabolas y = x2 + px + q (q ≠ 0) whose graphs cut the axes in three points. The family of circles through these three points have a common point
- (1, 0)
- (0, 1)
- (1, 1)
- None of these
The correct answer is: (0, 1)
Let the curve y = x2 + px + q cuts x-axis at A(
1, 0) and B (2,0) then 1+ 2= – p,
12= q also y = x2 + px + q cuts y-axis at C(0,q).
family of circles passing through A, B and C is
(x – 1) (x – 2) + y2 +
y = 0
where = –(1+q)
x2 + y2 + px + q – (1 + q) y = 0 is the equation of family of circles which always passes through (0, 1).
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