SOLUTION: find the equation of a circle of radius 'a' which passes through the two points on the axis of x which are at a distance b from origin

Question 810677: find the equation of a circle of radius 'a' which passes through the two points on the axis of x which are at a distance b from origin

Answer by josgarithmetic(39623) (Show Source): You can put this solution on YOUR website!
If both x-intercepts are b distance from the Origin, then looking at a picture or graph of this circle should show that the center is on the y-axis. Can you identify an isosceles triangle?

The center is some point, (0, c), and since you have a variable for radius, you may have a circle, . We really do not know if c is positive or if c is negative. We should try to obtain an equation in terms of b, but not with the variable c.

We know two points which are on the circle are (-b,0) and (b,0).
Either one, x^2 will be positive.
Use the point(s) in the equation:

, using the positive square root just to be simple.

Putting this c into the equation,

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