New In our Forum

Re: Reflecting graphs by flagator0012

Re: help with a question by flagator0012

Math Video Game! Play Decimals in Space! Use your reflexes & mathematical knowledge to shoot the right rocks!

A+

A−

Home Page

Algebra

Games

Geometry

Interactive

Trigonometry

Forum

Math Jobs

Top Topics in our Forum'

Topic	Views
Complex Numbers	5736
Proofs.	1851
Is the empty set a proper subset of the empty set?	2477
Absolute value question	3578
Area of Triangle	3741
Convert 324 from base 5 to base 10	2119
x congruency mod 6???	1866
complex numbers	471
How do I find missing angle measures?	4193
find the center and radius of circle (graphing)	1026

Equation of a Circle

Standard form equation of a Circle

This page: Angle formed by intersecting chords | Tangent and Chord||The perpendicular Bisector of a chord| Chords Equidistant from Center | product segments of intersecting chords
Related Pages: Circles forumula, graph, equations | Equation of A Circle | Circumference | Area | Chord |Arc | Inscribed Angles|Secant of circle | 2 Tangents from 1 point | Tangents, Secants, Circles Theorems

The standard form equation of a circle is a way to express the definition of a circle on the coordinate plane.

Remember that a circle is a locus of points. A circle is all of the points that are a fixed distance, known as the radius, from a given point, known as the center of the circle.
On the coordiante plane, the formula becomes (X-H)² + (Y-K)²=r²

h and k are the x and y coordines of the center of the circle
(x-9)² + (y-6)²=100 is a circle centered at (9,6) with a radius of 10

Definition of Circle

Definition: A circle is the set of all points that are the same distance, r, from a fixed point.
General Formula: X ² + Y ²=r²where r is the radius

Unlike parabolas, circles ALWAYS have X ² and Y ² terms.

X² + Y²=4 is a circle with a radius of 2 ( since 4 =2²)

On the coordiante plane, the formula is similar.

Interactive Circle

Interactive equation of circle activity. Click and drag either of the points below to explore the standard form equation of a circle and its relationship to the radius.

Practice Problems

What is the equation of the circle pictured on the graph below?
Picture of Equation of circle in standard form

Answer

Look at the graph below, can you express the equation of the circle in standard form?
Picture of Equation of circle in standard form

Answer

Look at the graph below, can you express the equation of the circle in standard form?

Answer
Picture of Equation of circle in standard form

Y²+X² =9
Y²+X² =16
Y²+X² =25
Y²+X² =36
Y²+X² =49

What is the radius of the circles on the left?

Radius of Circles

Equation of Circle in Standard Form

(y-3)²+(X-1)² =9
(y-5)²+(X-14)² =16
(y-1)²+(X-5)² =25
(X+2)²⁺+(y-12)² =36
(y+7)²+(X +5)² =49
(X +8)²+(y+17)² =49

What is the center and radius of each circle to the left?

Answers

(1, 3) r = 3
(14, 5) r = 4
(5, 1) r = 5
(-2, 12) r = 6
(-5, -7) r = 7
(-8, -17) r = 7

Top

Welcome Guest
Please Log in or register
Who's online: 4 Guests, 0 Users : Please welcome newlove08, our newest member.