# Show What You Know

### Bobby Manning Kemper 3

## Situation: Whispering Gallery

As a result of their unique elliptical shapes, whispering galleries enable the smallest sound generated at one

focus to be carried across the room to the other focus. The whispering gallery at the Chicago Museum of

Science and Industry is 47 ft 4 in long and 14 ft 6 in wide.

## Sypnosis

To find the equation of an ellipse you must first find the vertices and co-vertices. The vertices are the two points of the longer side of the ellipse. Calculate the distance from the center of the ellipse to that point and you will get the number you would use for your vertices The co-vertices are the two points of the shorter side of the ellipse, you will find them the same way you found the vertices. Once you have the vertices and co-vertices and the center you will plug the numbers into the standard ellipse formula which is (ysquared-k)/asquared + (xsquared-h)/bsquared. The letters h and k is the center of your circle and asquared is the vertices and bsquared is the co-vertices. You simply plug the numbers into the equation and that is it.

## Situation: Orbit of Venus

The orbit of Venus is nearly circular. An astronomer develops a model for the orbit in which the Sun has

coordinates (-5, 20), the circular orbit of Venus passes through (62, 20), and each unit of the coordinate plane

represents 1 million miles.

## Graph and Math

Center is at (-5,20)

Equation of the circle is (x+5)squared + (y-20)squared

Venus is 67 million miles away from the sun

It takes Venus 1,4095.46 million miles to orbit around the sun

## Sypnosis

The regular equation of a circle is (x-h)squared + (y-k)squared=rsquared. H and K both represent the center of the circle again and r represents the radius. To find the radius you must use the distance equation which is D=squareroot((x2-x1)+(y2-y1)squared). Once you have the center and radius you just simply plug them into the equation and you're done.