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### Course: Algebra (all content)>Unit 17

Lesson 5: Center and radii of an ellipse

# Ellipse graph from standard equation

This video explains how to graph an ellipse when given its equation in standard form. The center of this ellipse is (4,1), the horizontal radius is 4, and the vertical radius is 7. The key definitions are center, horizontal radius, and vertical radius.

## Want to join the conversation?

• hey, just asking, but in my math curriculum we had something like this, 3[x-1] squared, plus 3[y plus 3] squared. anybody understand?
(1 vote)
• You have 3(x-1)²+3(y+1)², and I assume this was set equal to a constant. I'll name the constant "3r²".
So 3(x-1)²+3(y+1)²=3r²
Divide by 3 and get (x-1)²+(y+1)²=r²
So this is the equation of a circle centered at (1, -1) with a radius of r.
• Can you go over a question that is more complicated? I get the basics but I need more help on the intermediate stuff. Thanks!
• hey guys an ellipse has a as length of 'radius' parallel to the horizontal axis
and b the 'radius' parallel to the vertical axis, while a hyperbola has a as whichever a or b is larger, right? it's still x^2/a^2 except a is always larger than b, right?
• For an ellipse, either the a or the b can be greater. When they are equal it forms a circle.
• An ellipse has an infinite number of radii like circles, or just two ?
(1 vote)
• There is no segment called the radius in an ellipse. The definition of a circle is the set of all points equidistant from a fixed point called the center (this distance is the radius). The definition of an ellipse is the set of all points such that the sum of the distances from two fixed points called the foci (plural of focus) is constant.

Imagine having two nails in a board. If you tie a string at each end to the nails and pull the string taught with your finger, you can trace an ellipse with your finger by moving it around while keeping the string taught (though you'd have to lift up the string over the nail when crossing one of the vertices). The length of the string obviously doesn't change. That length is the defining characteristic of the ellipse (along with the foci - where you place the two nails in the board).