• Skip to main content
  • Skip to secondary menu
  • Skip to primary sidebar
  • Skip to footer
  • ICSE Solutions
    • ICSE Solutions for Class 10
    • ICSE Solutions for Class 9
    • ICSE Solutions for Class 8
    • ICSE Solutions for Class 7
    • ICSE Solutions for Class 6
  • Selina Solutions
  • ML Aggarwal Solutions
  • ISC & ICSE Papers
    • ICSE Previous Year Question Papers Class 10
    • ISC Previous Year Question Papers
    • ICSE Specimen Paper 2021-2022 Class 10 Solved
    • ICSE Specimen Papers 2020 for Class 9
    • ISC Specimen Papers 2020 for Class 12
    • ISC Specimen Papers 2020 for Class 11
    • ICSE Time Table 2020 Class 10
    • ISC Time Table 2020 Class 12
  • Maths
    • Merit Batch

A Plus Topper

Improve your Grades

  • CBSE Sample Papers
  • HSSLive
    • HSSLive Plus Two
    • HSSLive Plus One
    • Kerala SSLC
  • Exams
  • NCERT Solutions for Class 10 Maths
  • NIOS
  • Chemistry
  • Physics
  • ICSE Books

Equation of Circles

December 9, 2020 by sastry

Equation of Circles

Let’s review what we already know about circles.
Definition: A circle is a locus (set) of points in a plane equidistant from a fixed point.

Equation of Circles 1

Now, if we “multiply out” the above example (x-2)2 + (y+5)2  = 9 we will get:

(x-2)2 + (y+5)2  = 9
(x2-4x+4) +( y2+10y+25) = 9
x2-4x+4+ y2+10y+25 = 9
x2+ y2-4x+10y+20= 0
x2+y2+Cx+Dy+E = 0

When multiplied out, we obtain the “general form” of the equation of a circle. Notice that in this form we can clearly see that the equation of a circle has both x2 and y2 terms and these terms have the same coefficient (usually 1).

When the equation of a circle appears in “general form”, it is often beneficial to convert the equation to “center-radius” form to easily read the center coordinates and the radius for graphing.
Equation of Circles 2

Examples:

1. Convert x2+ y2-4x-6y+8= 0  into center-radius form.

This conversion requires use of the technique of completing the square.

We will be creating two perfect square trinomials within the equation.

Equation of Circles 3

  • Start by grouping the x related terms together and the y related terms together. Move any numerical constants (plain numbers) to the other side.
  • Get ready to insert the needed values for creating the perfect square trinomials. Remember to balance both sides of the equation.
  • Find each missing value by taking half of the “middle term” and squaring. This value will always be positive as a result of the squaring process.
  • Rewrite in factored form.
    You can now read that the center of the circle is at (2, 3) and the radius is /5

2. How do the coordinates of the center of a circle relate to C and D when the equation of the circle is in the general form x2+ y2+Cx+Dy+E = 0.

Let’s make some observations. Re-examine our previous equations in general form and center-radius form. Do you see a relationship between the center coordinates and C and D?

Equation of Circles 4

Equation of Circles 5

3. Write the equation of a circle whose diameter has endpoints (4, -1) and (-6, 7).

Equation of Circles 6

4. Write the equation for the circle shown below if it is shifted 3 units to the right and 4 units up.

A shift of 3 units to the right and 4 units up places the center at the point (3, 4). The radius of the circle can be seen from the graph to be 5.
Equation:(x-3)2 + (y-4)2  = 25

5. Convert 2x2+ 2y2+6x-8y+12= 0 into center-radius form.

Whoa!!! This equation looks different. Are we sure this is a circle???
In this equation, both the x and y terms appear in squared form and their coefficients (the numbers in front of them) are the same. Yes, we have a circle here! We will, however, have to deal with the coefficients of 2 before we can complete the square.

Equation of Circles 7

Filed Under: Mathematics Tagged With: Equation of Circles

Primary Sidebar

  • MCQ Questions
  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • ICSE Solutions
  • Selina ICSE Solutions
  • Concise Mathematics Class 10 ICSE Solutions
  • Concise Physics Class 10 ICSE Solutions
  • Concise Chemistry Class 10 ICSE Solutions
  • Concise Biology Class 10 ICSE Solutions
  • Concise Mathematics Class 9 ICSE Solutions
  • Concise Physics Class 9 ICSE Solutions
  • Concise Chemistry Class 9 ICSE Solutions
  • Concise Biology Class 9 ICSE Solutions
  • ML Aggarwal Solutions
  • ML Aggarwal Class 10 Solutions
  • ML Aggarwal Class 9 Solutions
  • ML Aggarwal Class 8 Solutions
  • ML Aggarwal Class 7 Solutions
  • ML Aggarwal Class 6 Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC

Recent Posts

  • Air Pollution Essay for Students and Kids in English
  • 10 Lines on Satya Nadella for Students and Children in English
  • Essay on Wonders of Science | Wonders of Science for Students and Children in English
  • My Childhood Memories Essay | Essay on My Childhood Memories for Students and Children in English
  • Essay On Sports And Games | Sports And Games Essay for Students and Children in English
  • Clean India Slogans | Unique and Catchy Clean India Slogans in English
  • Animals that Start with Z | Listed with Pictures, List of Animals Starting with Z & Interesting Facts
  • Positive Words That Start With S | List of Positive Words Starting With S Meaning, Examples,Pictures and Facts
  • Positive Words that Start with B | List of 60 Positive Words Starting with B Pictures and Facts
  • Humanity Essay | Essay on Humanity for Students and Children in English
  • Teenage Pregnancy Essay | Essay on Teenage Pregnancy for Students and Children in English

Footer

  • RS Aggarwal Solutions
  • RS Aggarwal Solutions Class 10
  • RS Aggarwal Solutions Class 9
  • RS Aggarwal Solutions Class 8
  • RS Aggarwal Solutions Class 7
  • RS Aggarwal Solutions Class 6
  • Picture Dictionary
  • English Speech
  • ICSE Solutions
  • Selina ICSE Solutions
  • ML Aggarwal Solutions
  • HSSLive Plus One
  • HSSLive Plus Two
  • Kerala SSLC
  • Distance Education
DisclaimerPrivacy Policy
Area Volume Calculator