How to Find the Equation of a Circle with Given Points and Radius?

[Dumbledore211]

Homework Statement

Find the equation of the circle which intersects the x-axis at two points at 2 unit distance from the origin and the radius is 5

Homework Equations

x^2 + y^2 + 2gx + 2fy + c=0

r=(g^2+f^2-c)^1/2

The Attempt at a Solution

I first tried to solve it by assuming that the two points are (2,0) and (2+x,0). The main conundrum is solving for x and also finding out the center of the circle

 

[tiny-tim]

Hi Dumbledore211!

Find the equation of the circle which intersects the x-axis at two points at 2 unit distance from the origin …

No, they're both at 2 from the origin, so they're x = ±2.

(and so the centre will … ?)

 

[Tanya Sharma]

Homework Statement

Find the equation of the circle which intersects the x-axis at two points at 2 unit distance from the origin and the radius is 5

Homework Equations

x^2 + y^2 + 2gx + 2fy + c=0
(x-g)^2 + (y-h)^2= r^2

The Attempt at a Solution

I first tried to solve it by assuming that the two points are (2,0) and (2+x,0). The main conundrum is solving for x and also finding out the center of the circle

The two points on the x- axis at 2 unit distance from the origin are (-2,0) and (2,0) . I guess now it should be easy for you

 

[Dumbledore211]

Thank you. It should be fairly easy to solve it using your helpful info