Conics - Circle

Get the most by viewing this topic in your current grade. Pick your course now.

Examples
Lessons
  1. graphing a circle
    Sketch each circle and state the:
    i) center
    ii) radius
    1. (x53)2+(y+43)2=1{\left( {\frac{{x - 5}}{3}} \right)^2} + {\left( {\frac{{y + 4}}{3}} \right)^2} = 1
    2. 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
    1. Convert the equation to conics form.
    2. 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:
    1. center (3,  5)\left( { - 3,\;5} \right), radius = 7
    2. center (2,  0)\left( {2,\;0} \right), passing through the point (1,  4)\left( { - 1,\;4} \right)
    3. diameter with endpoints (9,  4)\left( { - 9,\;4} \right) and (15,  6)\left( {15,\; - 6} \right)
    4. center (2,  1)\left( { - 2,\; - 1} \right), tangent to the line 3x+4y=153x + 4y = 15
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun - with achievements, customizable avatars, and awards to keep you motivated.
  • Easily See Your Progress

    We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.
  • Make Use of Our Learning Aids

    Last Viewed
    Practice Accuracy
    Suggested Tasks

    Get quick access to the topic you're currently learning.

    See how well your practice sessions are going over time.

    Stay on track with our daily recommendations.

  • Earn Achievements as You Learn

    Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.
  • Create and Customize Your Avatar

    Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
Topic Notes

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