When is an ellipse a circle

There are many points you could choose. Plugging this into the equation, we get:. The left side is equal to the right side of the equation, and so this is a valid point on the circle. Now, complete the square in both parentheses, subtracting or adding the necessary constant to both sides of the equation:.

It even has a number on the right side. How can we get rid of them to get into standard form? Privacy Policy.

Skip to main content. Conic Sections. Search for:. The Circle and the Ellipse. Learning Objectives Explain how the equation of a circle describes its properties. Key Takeaways Key Points A circle is defined as the set of points that are a fixed distance from a center point. The distance formula can be extended directly to the definition of a circle by noting that the radius is the distance between the center of a circle and the edge. Key Terms diameter : Two times the radius of a circle.

Learning Objectives Connect the equation for an ellipse to the equation for a circle with stretching factors. Key Takeaways Key Points An ellipse and a circle are both examples of conic sections. It works because the string naturally forces the same distance from pin-to-pencil-to-other-pin. An ellipse is the set of all points on a plane whose distance from two fixed points F and G add up to a constant. The Major Axis is the longest diameter. It goes from one side of the ellipse, through the center, to the other side, at the widest part of the ellipse.

And the Minor Axis is the shortest diameter at the narrowest part of the ellipse. Email Required, but never shown. Upcoming Events. Featured on Meta. Now live: A fully responsive profile. The unofficial elections nomination post. Related 9. Hot Network Questions.

Question feed. Mathematics Stack Exchange works best with JavaScript enabled. If the foci are relatively far away from the center, the ellipse is shaped more like an oval, and e is closer to one. A circle is the collection of points equidistant from a fixed point. The fixed point is called the center. The distance from the center to any point on the circle is the radius of the circle, and a segment containing the center whose endpoints are both on the circle is a diameter of the circle.

The radius, r , equals one-half the diameter, d. The radius is r.