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Graphing circles from features

How to graph a circle given the center and either the radius or another point on the circle.

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  • blobby green style avatar for user madhavi vishnubhotla
    what should be the exact angle between the plane and cone to get a parabola?
    (15 votes)
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    • aqualine ultimate style avatar for user Lau Sky
      Basically if you have a cone like and you slice it straight in half parallel to the ground you get a circle. Like slicing a cone on the line "A". But if you slice it perpendicular to the ground you get a hyperbola. If you slice it on a slan (0 to 90 degrees) t you can either get a ellipse or a parabola. An ellips will be from cutting the cone near the top so you can get the full circle. If you cut it on a slant near the bottom section it will be like getting an unfinished ellipse or parabola.
      (4 votes)
  • duskpin sapling style avatar for user viktoria ngo
    when I try solving the problem, I can not extend the circle I order to make the radius larger
    (2 votes)
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  • leafers tree style avatar for user Molly
    Is this on a cartesian plane? why is it that I can't graph ellipses on my graphing calculator? Is it because they aren't functions?
    (2 votes)
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    • starky ultimate style avatar for user KLaudano
      This is graphed on the cartesian plane.

      Circles and ellipses are not functions, so graphing calculators will not usually be able to graph the equations directly. However, you can split the circle/ellipse equation into the top and bottom halves which are functions and can be graphed.
      (2 votes)
  • hopper cool style avatar for user π guy
    I'm a bit confused on couldn't you have a circle that is bigger than that and still include the point (0,4) or does the outline of the circle actually have to touch this point?
    (1 vote)
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    • leaf green style avatar for user kubleeka
      When we talk about 'circles', we're referring only to the outer edge of the shape, not the outer edge plus interior. So we can say things like 'a line intersects a circle in at most two points' which wouldn't be true if we included the interior.

      If we mean to include the interior in our discussion, we use the word 'disk'.
      (4 votes)
  • starky ultimate style avatar for user lloyd whittington
    Can a circle be considered a degenerate form of an ellipse?
    (2 votes)
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  • blobby green style avatar for user rinal28746
    how do I add another point on to the circle while graphing
    (1 vote)
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  • blobby green style avatar for user Haneeth Devangam
    find the eq of the tangent drawn from the origin to the circle (x*x)+(y*y)+(2gx)+2fy+c=0 and hence deduce a condition for these tangents to be perpendicular
    (1 vote)
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  • female robot amelia style avatar for user malavika228
    the point (0,4) for the circle radius was given but why wasn't the circle on the x axis point zero? sorry, just a bit confused
    (1 vote)
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  • blobby green style avatar for user Theresa Lambayon
    How can I construct a table of values?
    Am I the one to contruct it?
    (1 vote)
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    • male robot hal style avatar for user Madd Sam
      A table of values for graphing a function? It usually consists of two columns. One may be headed "x", and the other f(x). Under x, you list different values for x. Then plug each of these values into the function and the output value will be f(x). Make sure you keep each x lined up next to its corresponding f(x) value.
      (1 vote)
  • duskpin ultimate style avatar for user FemiO
    At , he could have used the distance formula to find the radius, and the equation of the circle to help. Why didn't he us it?
    (1 vote)
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    • piceratops ultimate style avatar for user Hecretary Bird
      Simply because the question didn't require him to go and make an equation, and it's faster without it. Using the distance formula to create an equation and graphing based on that is a valid solution, but lots more tedious than just plotting the circle's center and using a point the question tells you is on the circle to draw the circle.
      (1 vote)

Video transcript

- [Voiceover] We're asked to graph the circle which is centered at 3, -2 and has a radius of 5 units. I got this exercise off of the Khan Academy graph a circle according to its features exercise. It's a pretty neat little widget here, because what I can do is I can take this dot and I can move it around to redefine the center of the circle so it's centered at 3, -2. So, X is 3 and Y is -2, so that's its center. It has to have a radius of 5. The way it's drawn right now it has a radius of 1. The distance between the center and the actual circle, the points that define the circle, right now it's 1. I need to make this radius equal to 5. If I take that, so now the radius is equal to 2, 3, 4 and 5. There you go. Centered at 3, -2, radius of 5. Notice you go from the center to the actual circle it's 5 no matter where you go. Let's do one more of these. Graph the circle which is centered at -4, 1 and which has the point 0, 4 on it. Once again, let's drag the center, so it's going to be -4, X is -4. Y is 1, so that's the center. It has the point 0, 4 on it. X is 0, Y is 4. I have to drag, I have to increase the radius of the circle. Let's see, whoops, nope, I want to make sure I don't change the center. I want to increase the radius of the circle until it includes this point right over here, 0,4. I'm not there quite yet, there you go. I'm now including the point 0, 4. If we're curious what the radius is, we could just go along the X axis. X = -4 is the X coordinate for the center and we see that this point ... This is -4,1 and we see that 1,1 is actually on the circle. The distance here is you go 4 then another 1, it's 5. This has a radius of 5. But either way, we did what they asked us to do.