Hello,

So today I will blog about circles and ellipses.

First Circles ,I hope we all know what circles are, but if not circles can be defined as a set of points that are a given distance from a given point. The general equation of a circle is (x-h)^2+(y-k)^2=r^2. H and K is the center of the circle, remember that the H and K value are the opposite sign so if a given circle was located at (-3,4) it would read (x+3) and (y-4). The radius or R, is the distance from the center to any point on the circle. It is important to remember that when given an equation the R value must be square-rooted because it had been squared when R was put in to the equation. For example, if a given equation was (x+1)^2+(y-2)=16, then the radius would be 4 because the square root of 16 is 4.

Next is ellipses, ellipses are similar to circles except that not all points on the ellipses are equal distance from the center (there is no radius). The equation is (x-h)^2/a^2 + (y-k)^2/b^2. Again H and K are the center of the ellipse. 'A' represents the horizontal distance from the center, and B represents the vertical distance from the center. Remember again that H and K are the opposite signs of what is in the equation. An easy way to remember if the ellipses is horizontal or vertical is if; A greater than B than it is horizontal, and B is greater than A then it is vertical. You may notice that if the value of A and B are the same, then the equation turns into the circle equation. That being said if A and B are the same it forms a circle. This

is the case because a circle is actually a special case of an ellipses.

Ellipses are actually all over the place! Planets orbit in an elliptical way, the electrons also move elliptically around the nucleus. Have you ever heard of whispering galleries? This is when you whisper in one focal point in a building and at another focal point across the room you can hear the person as though they are standing right beside you, this occurs because the building is an ellipse.

Thank you for your time,

KG