Geo4.18

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Find the circle which passes through (-1,2),(3,-2) and has its centre on the line x-2y=0\,

Let the equation of the circle be

x^{2}+y^{2}+2gx+2fy+c=0\,

The point (-1,2) lies on the circle,hence

1+4-2g+4f+c=0\,

-2g+4f+c=-5\,

Point (3,-2) lies on the circle

9+4+6g-4f+c=0\,

6g-4f+c=-13\,

Also the centre lies on x-2y=0\,

Hence

-g+2f=0\,

g=2f\,

Substituting this in the first equation we get

-2(2f)+4f+c=-5\,

c=-5\,

Now

6(2f)-4f-5=-13\,

8f=-8\,

Hence f=-1, Now g=-2

Equation of the circle is

x^{2}+y^{2}-4x-2y-5=0\,


Main page:Geometry:Circles