Graphing a Circle: Find Center, Radius & Intercepts

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Homework Help Overview

The problem involves finding the center, radius, and intercepts of a circle represented by the equation x^2 + y^2 – x + 2y + 1 = 0. The subject area is analytic geometry, specifically focusing on the properties of circles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster expresses confusion about how to approach the problem, mentioning attempts to plug in numbers. Some participants discuss the transition from general form to standard form and the method of completing the square.

Discussion Status

Some participants have suggested a potential standard form of the circle's equation and identified the center and radius based on that form. However, there is no explicit consensus on the overall approach or the final interpretation of the problem.

Contextual Notes

The original poster indicates a lack of clarity on the problem-solving process, and there may be assumptions about prior knowledge of completing the square that are not explicitly stated.

elitespart
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Consider x^2 + y^2 – x + 2y + 1 = 0.
(a) Find the coordinates of the center and the length of the radius.
(b) Determine the coordinates of the intercepts.
(c) Graph the circle.



I'm really lost on this one. I tried plugging in numbers but I seriously doubt that's how I'm supposed to do it. Can someone point me in the right direction? Thanks
 
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Standard Form versus General Form.
Completing the Square.
 
oh so just (x-1/2)^2 + (y+1)^2 = 1/4? center would be at (1/2, -1) and radius is sqrt(1/4)=(1/2)?
 
elitespart said:
oh so just (x-1/2)^2 + (y+1)^2 = 1/4? center would be at (1/2, -1) and radius is sqrt(1/4)=(1/2)?

Yup! :biggrin:
 

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