Ellipses What do they look like Like stretchedout
- Slides: 8
Ellipses …
What do they look like? • Like stretched-out circles • “Oval”
Why do we care? �Biggest reason? We’re zooming around in one right now. The orbit of planetary bodies follows elliptical paths Being able to map orbits allows us to calculate meteor showers, debris impact, etc.
So what’s the deal with ellipses? �They are symmetrical vertically and horizontally �They have a definite center �So far, it’s like a circle. How is it different? �No one radius �Instead, two focii
The focii �The sum of the distance from the focus to any point on the ellipse is going to be the same. �It’s going to be 2 a �Where a is also the distance from the center of the ellipse to the longer end.
More with focii �If we call the distance from the center to the long end a, we call the distance from the center to the short end b. �Here’s the fun part: �The distance from the center to the focus? �c �Where a 2 – b 2 = c 2
What about the equation? �Two of them – one for being stretched top to bottom, one for left to right �Left-right (horizontal) Top-bottom (vertical)
Summary �Center = (h, k) �Count to find the a and b. �Now you have the equation. �Find c using a and b. �For horizontal, focii are (h+c, k) and (h-c, k) �For vertical, focii are (h, k+c) and (h, k-c) �Axes length – 2 a is major, 2 b is minor.
