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Find the equation to the circle passing through the points (0,a)(b,h) and having its centre on the axis of x Pls give me full solution

Find the equation to the circle passing through the points (0,a)(b,h) and having its centre on the axis of x
Pls give me full solution

Grade:11

1 Answers

poojitha
42 Points
3 years ago
Let  x^2+y^2+2gx+2fy+c=0 is our required circle equation with centre (-g,-f).
since it passes through (0,a)and(b,h). substitute those points in circle equation.
(0,a)              a^2+2fa+c=0    is eq (1).                 (b,h)      b^2+h^2+2gb+2fh+c=0 is eq (2).
since centre lies on x-axis f=0.so from (1), c=-a^2.
on substituting c and f values in eq(2),we get g = [a^2-(b^2+h^2)]/2b
on substituting these values in circle equation we get
b(x^2+y^2)+[a^2-(b^2+h^2)]x-a^2b=0 is our required circle equation.

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