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

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Homework Help Overview

The discussion revolves around finding the equation of a circle that intersects the x-axis at two points, each 2 units from the origin, with a specified radius of 5. The problem involves understanding the geometric properties of circles and their equations.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants explore the coordinates of the intersection points on the x-axis, with some suggesting that these points are (-2,0) and (2,0). There is also a focus on determining the center of the circle and how to apply the given radius in the context of the problem.

Discussion Status

The discussion has seen participants clarifying the positions of the intersection points and considering the implications for the circle's center. Some guidance has been provided regarding the coordinates, which may help in progressing towards a solution.

Contextual Notes

There is an emphasis on the radius and the specific distance of intersection points from the origin, which may influence the approach to finding the equation. The original poster's assumptions about the points and their implications are under examination.

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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
 
Last edited:
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Hi Dumbledore211! :smile:
Dumbledore211 said:
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. :wink:

(and so the centre will … ?)
 
Dumbledore211 said:

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

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