Find the Equation of the Circle which passes through 2 points on x - axis which are at a distance of 4 units from origin and whose radius is 5 units

The general equation of the circle is,
x2+y2+2gx+2fy+c=0... (1)
The two points on the x-axis are at the distance of 4 units from the orgin.
So the points can be (4, 0) and (-4, 0).
So (1) passes through these 2 points.
4,042+02+2g. 4+ 2f.0+c=016+8g+c=0 ... 2-4,0-42+02+2g. -4+ 2f.0+c=016-8g+c=0 ... 3Adding 2 and 3 we get,32+2c=0c=-322=-16From (2),16+8g -16=08g=0g=0Given tht radius = 5g2+f2-c=502+f2--16=5f2+16=25f2=9f=±3Substituting g, f and c values in (1),x2+y2+2x. 0+2y. ±3-16=0x2+y2±6y-16=0

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