In Exercises 21-28 , sketch the circle. Identify its center and radius. x^2+6 x+y^2-12 y+41=0

Name: Problem 26, Chapter 9: Precalculus with Limits : A Graphing Approach
Uploaded: 2020-09-08T14:25:42-08:00
Duration: 3 min 15 s
Channel: Suman Saurav Thakur
Description: In Exercises 21-28 , sketch the circle. Identify its center and radius. x^2+6 x+y^2-12 y+41=0

step 1 We have 26 number question. The equation is x square plus 6x plus y square minus 12 y plus 41 eq

In Exercises 21-28 , sketch the circle. Identify its center...

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Key Concepts

Standard Form of a Circle

The standard form of a circle's equation is written as (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r is its radius. This form makes it easy to extract the geometric properties needed for graphing and analyzing the circle.

Completing the Square

Completing the square is a technique used to transform a quadratic equation into a perfect square trinomial, which helps in rewriting the equation in the standard form of a circle. This method plays a crucial role in identifying the center and radius of the circle from its general equation.

Identification of Center and Radius

By converting the general equation of a circle into its standard form through completing the square, one can directly read off the coordinates of the center (h, k) and determine the radius r from the equation. This identification is fundamental in sketching the circle accurately on the coordinate plane.

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