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### Course: High school geometry>Unit 7

Lesson 1: Graphs of circles intro

# Graphing circles from features

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

## Want to join the conversation?

• what should be the exact angle between the plane and cone to get a parabola?
• 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.
• Can a circle be considered a degenerate form of an ellipse?
• Yes. To quote Wolfram Alpha, the circle is a degenerate form of an ellipse as the eccentricity approaches 0.
• when I try solving the problem, I can not extend the circle I order to make the radius larger
• Make sure the inner circle is not "highlighted" or in its larger size. Then grab the outer circle with the cursor and see if it will extend. It took me a while to get the hang of it, but it does work. Good luck!
• how do I add another point on to the circle while graphing
• There is no need to. But could you explain more thoroughly?
• 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?
• 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.
• 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
• Is this a problem you are trying to solve?
• 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
• The center is just a point, the coordinates for a point is simply (x,y), how much you move on the horizontal and how much you move on the vertical axis, so (0,4), you move 0 units on the x axis and 4 units on the y axis, that's why it is a up there.
• 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)
• 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'.