Can you go over a question that is more complicated? I get the basics but I need more help on the intermediate stuff. Thanks!

Hello, if you would like to learn more about conic sections in higher detail, check out this book. https://artofproblemsolving.com/store/item/intermediate-algebra

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?

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.

An ellipse has an infinite number of radii like circles, or just two ?

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).

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Precalculus

Course: Precalculus > Unit 5

Lesson 2: Center and radii of an ellipse

Ellipse graph from standard equation

Name: Ellipse graph from standard equation
Uploaded: 2016-03-17T03:39:03Z
Description: 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.

Google Classroom

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.

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shafferdprogrammer
Posted 6 years ago. Direct link to shafferdprogrammer's post “hey, just asking, but in...”
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?
Button navigates to signup pageComment on shafferdprogrammer's post “hey, just asking, but in...”
(1 vote)
Answer
- kubleeka
  Posted 6 years ago. Direct link to kubleeka's post “You have 3(x-1)²+3(y+1)²,...”
  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.
  Button navigates to signup page
  (9 votes)
Jordan Law
Posted 6 years ago. Direct link to Jordan Law's post “Can you go over a questio...”
Can you go over a question that is more complicated? I get the basics but I need more help on the intermediate stuff. Thanks!
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(4 votes)
Answer
- sabysagar
  Posted 4 years ago. Direct link to sabysagar's post “Hello, if you would like ...”
  Hello, if you would like to learn more about conic sections in higher detail, check out this book.
  https://artofproblemsolving.com/store/item/intermediate-algebra
  Button navigates to signup page
  (2 votes)
Kevin S.
Posted 4 years ago. Direct link to Kevin S.'s post “hey guys an ellipse has a...”
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?
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(4 votes)
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- Matthew Johnson
  Posted 3 years ago. Direct link to Matthew Johnson's post “For an ellipse, either th...”
  For an ellipse, either the a or the b can be greater. When they are equal it forms a circle.
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  (0 votes)
Mohamed Ibrahim
Posted 4 years ago. Direct link to Mohamed Ibrahim's post “An ellipse has an infinit...”
An ellipse has an infinite number of radii like circles, or just two ?
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(1 vote)
Answer
- Christopher Blake
  Posted 4 years ago. Direct link to Christopher Blake's post “There is no segment calle...”
  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).
  Button navigates to signup page
  (2 votes)
Peterson Torio
Posted 4 years ago. Direct link to Peterson Torio's post “How would you write an eq...”
How would you write an equation for ellipses if it is tilted?
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(1 vote)
Answer
- Guineacow
  Posted 10 months ago. Direct link to Guineacow's post “To do that, you probably ...”
  To do that, you probably should do the trig thing to get the horizontal and vertical radius.
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  (1 vote)
onyinyechukwu.monyei
Posted 4 years ago. Direct link to onyinyechukwu.monyei's post “write an equation for an ...”
write an equation for an ellipse if the endpoints of the major axis are at (1,6) and (1,-6) and the endpoints of the minor axis are at (5,0) and (-3,0)
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(0 votes)
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Video transcript

- [Voiceover] We're asked which ellipse is represented by the equation x minus four squared over 16 plus y minus one squared over 49 is equal to one. And we're given a bunch of choices here. We're given four choices here. So let's just think about what's going on here. So the center of the ellipse is going to be four comma one. How do I know that? Well the equation of the ellipse is going to be x minus the x-coordinate for the center squared over here, over the horizontal axis is horizontal radius squared plus y minus the y-coordinate of the center squared over the vertical radius squared. So the center is going to be four comma one. So the center here is not four comma one. The center over here is not four comma one. Not four comma one. The only choice that has a center at four comma one is this one over here. So we already know this is the choice without even looking at the horizontal and the vertical radius. But we can verify that this works out 'cause a horizontal radius right over here, notice it goes this orange line, which can represent the horizontal radius. It has a length of four and so the horizontal radius is four and so we see indeed that 16 is the horizontal radius squared, this is four squared. And if we look at the vertical radius here, we see it has a length of seven. We're going from y equals one to y equals eight, has a length of seven. And we see in that equation that this indeed is seven squared. So that was pretty straight forward.