Let x 2 + y 2 + Ax + By + C = 0 be a circle passing through (0, 6) and touching the parabola y = x 2 at (2, 4). Then A + C is equal to______.
Text Solution
Verified by ExpertsA
x 2 + y 2 + Ax + By + C = 0 is passing through (0,6)
6B + C = -36
The tangent of the parabola y = x 2 at (2, 4) is
4x-y-4 = 0 …(1)
The tangent of circle x 2 + y 2 + Ax + By + C = 0 at (2, 4) is
(4 + A) x + ( 8 + B)y + 2A + 4B +2C = 0 …(2)
From Equation (1) and (2)
A + 4B = -36 ….(3)
3A + 4B + 2C = -4 ….(4)
From equation (3) and (4) A+C= 16
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