Conics - Circle

Conics - Circle

Lessons


distance formula, midpoint formula and circle
The conics form of a circle with center (h,k)\left( {h,\;k} \right) and radius rr is:
(xhr)2+(ykr)2=1{\left( {\frac{{x - h}}{r}} \right)^2} + {\left( {\frac{{y - k}}{r}} \right)^2} = 1
  • 1.
    graphing a circle
    Sketch each circle and state the:
    i) center
    ii) radius
    a)
    (x53)2+(y+43)2=1{\left( {\frac{{x - 5}}{3}} \right)^2} + {\left( {\frac{{y + 4}}{3}} \right)^2} = 1

    b)
    x2+y2=25{x^2} + {y^2} = 25


  • 2.
    converting a circle equation to conics form by “completing the square”
    4x2+4y2+24x8y+15=04{x^2} + 4{y^2} + 24x - 8y + 15 = 0
    a)
    Convert the equation to conics form.

    b)
    Sketch the graph and state the:
    i) center
    ii) radius


  • 3.
    finding the equation of a circle given its properties
    Find the equation of a circle with:
    a)
    center (3,5)\left( { - 3,\;5} \right), radius = 7

    b)
    center (2,0)\left( {2,\;0} \right), passing through the point (1,4)\left( { - 1,\;4} \right)

    c)
    diameter with endpoints (9,4)\left( { - 9,\;4} \right) and (15,6)\left( {15,\; - 6} \right)

    d)
    center (2,1)\left( { - 2,\; - 1} \right), tangent to the line 3x+4y=153x + 4y = 15


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