Equation of Circle: Centre (2,-4), y-intercept 1

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Homework Help Overview

The discussion revolves around finding the equation of a circle given its center at (2,-4) and a y-intercept at 1. Participants are exploring the relationship between the center, radius, and the y-intercept in the context of circle equations.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the standard form of the circle's equation and consider how to determine the radius using the provided y-intercept. There is also a mention of a related question about another circle intersecting the x-axis.

Discussion Status

The discussion is active, with participants engaging in clarifying the relationship between the circle's parameters. Some guidance has been offered regarding the use of the y-intercept to find the radius, and additional questions have been raised about a different circle scenario.

Contextual Notes

Participants are working under the constraints of a homework assignment, which may limit the information they can use or the methods they can apply. The original poster's follow-up question indicates a potential exploration of related concepts.

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Homework Statement



find the equation of a circle with centre of (2,-4) and y-intercept 1

Homework Equations





The Attempt at a Solution

 
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The equation of a circle of radius r centered at the point (a,b) is given by (x-a)2+(y-b)2=r2. Since you already are given the point (a,b), all you need to find is the radius of the circle. Can you use the information that a y-intercept is (0,1) to find the radius?
 
n!kofeyn said:
The equation of a circle of radius r centered at the point (a,b) is given by (x-a)2+(y-b)2=r2. Since you already are given the point (a,b), all you need to find is the radius of the circle. Can you use the information that a y-intercept is (0,1) to find the radius?

Thank you so much I didn't know it was that simple xD ok then can I ask something else:

A circle with a centre (5,4) intersects the x-axis 3 units from the origin. Find the possible equations of the circle.

Never mind i got it :D
 
Last edited:
Ok, cool!
 

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