Geo4.35

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Find the equation of the circle which passes through (1,-2),(3,-4) and touches the X-axis.

Let the equation of the circle be

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

The circle touches x-axis means c=g^{2}\,

It passes thro'(1,-2)

2g-4f+g^{2}=-5\,

Let this equation be 1.

Required circle passes through (3,-4)

6g-8f+g^{2}=-25\,

Let this equation be 2.

Solving the two equations,we get

-g^{2}+2g+15=0\,

Factoring

(g-5)(g+3)=0,g=5,-3\,

Hence c=25,9

The value of f is

2(5)-4f+25=-5,2(-3)-4f+9=-5\,

f=10,2\,

Hence the equations of the circle are

x^{2}+y^{2}+10x+20y+25=0,x^{2}+y^{2}-6x+4y+9=0\,


Main Page:Geometry:Circles