Question

Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle. $$ x^{2}+x+y^{2}-\frac{6}{5} y=1 $$

Name: Problem 12, Chapter 7: Precalculus
Uploaded: 2021-08-14T15:11:06-08:00
Duration: 2 min 16 s
Channel: Erika Bustos
Description: Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle. x^2+x+y^2-(6)/(5) y=1

   Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle.
$$
x^{2}+x+y^{2}-\frac{6}{5} y=1
$$

Precalculus

Carl Stitz, Jeff… 3rd Edition

Chapter 7, Problem 12

Instant Answer

Solved by Expert Erika Bustos

08/14/2021

Step 1

Step 1: First, we rewrite the given equation, leaving some space for the terms we will add to complete the square: $$ x^{2}+x+\_\_\_+y^{2}-\frac{6}{5} y+\_\_\_=1+\_\_\_+\_\_\_ $$ Show more…

Show all steps

Thanks for your feedback!

Complete the square in order to put the equation into standard form. Identify the center and the radius or explain why the equation does not represent a circle. $$ x^{2}+x+y^{2}-\frac{6}{5} y=1 $$

Play audio

Feedback

Erika Bustos and 101 other subject Precalculus educators are ready to help you.

Ask a new question

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Standard Form of a Circle

The standard form for a circle is (x - h)² + (y - k)² = r², where (h, k) represents the center and r is the radius. This form is useful because it clearly defines the circle's location and size, and any circle equation can be rearranged into this form by completing the square.

Center and Radius

Once the equation of a circle is expressed in its standard form, the center is given directly by the coordinates (h, k), and the radius is determined by taking the square root of the constant term on the right-hand side. This process simplifies the understanding and graphical representation of the circle.

Completing the Square

This is a method used to rewrite quadratic expressions as a perfect square plus or minus a constant. It involves adding and subtracting the necessary constant term to form a perfect square trinomial, thereby making it easier to identify specific properties of conic sections, such as the center and radius of a circle.

Please give Ace some feedback