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Show that the equation x^2 + y^2 - 2x - 2ay - 8 = 0 represents for different values of 'a' a sytem of circles passing through two fixed points a, b on the x - axis and find the equation of that circle of the system, the tangents to which at a, b meet on the line x + 2y + 5 = 0.

Show that the equation x^2 + y^2 - 2x - 2ay - 8 = 0 represents for different values of 'a' a sytem of circles passing through two fixed points a, b on the x - axis and find the equation of that circle of the system, the tangents to which at a, b meet on the line x + 2y + 5 = 0.

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
From Famile of circles,
Apply S1 + KL = 0
Where S1 = x^2 + y^2 - 2x - 2ay - 8 = 0
L =  x + 2y + 5 = 0
and then put y = 0.

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