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    Equation of a Circle

    Standard form equation of a Circle

    This page: Angle formed by intersecting chords | Tangent and Chord|Chord TheoremsThe 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 | Tangent |Arc of A Circle | Intersecting Chords |Inscribed Angle |Secant of circle | 2 Tangents from 1 point |Central Angle | Angles, Arc, Secants, tangents |Tangents, Secants and Side Lengths | Tangent and a Chord | images

    Free Math Printable Worksheets: Circles Worksheets and Activites for Math Teachers

    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 coordinate plane, the formula becomes (X-H)2 + (Y-K)2=r2
      • h and k are the x and y coordinates 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=r2 where 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 coordinate 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

     
     

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