Let the abscissae of the two points P and Q on a circle be the roots of x 2 - 4x - 6 = 0 and the ordinates of P and Q be the roots of y 2 + 2y - 7 = 0. If PQ is a diameter of the circle x 2 + y 2 + 2ax + 2by + c = 0, then the value of (a + b - c) is
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Equation of circle diameter form
(x – x 1 ) (x - x 2 ) + (y – y 1 ) (y - y 2 ) = 0
(where x 1 , x 2 are the roots of x 2 - 4x - 6 = 0 and y 1
y 2 are the roots of y 2 + 2y - 7 = 0
x + y - 4x + 2y-13 = 0
Now,
Compare it with the given equation, we get
a = -2, b = 1, c = -13
Now a + b – c = 12
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