An ellipse is a type of conic section whose equation is [math]1=\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}[/math]. Go through this worksheet investigating an ellipse and its equation. Use the interactive to help you, and answer each question to the best of your ability.
Describe what the similarities and differences between variables h and k when you change its values using the sliders.
Describe what the similarities and differences between variables b and a when you change its values using the sliders.
What happens when the values for the variables a and b are negative? Does the ellipse look different if the value for a is 1 or -1? What about if b is 1 or -1?
Are their any values for any of the variables that will not work? If so why do you think that is? (Hint: put the value into the equation)
What will happen if the values for a and b are the same? What shape does it make? (Use values other than 0)
If the center of the ellipse is correlated to the values of the variables of k and h, what do the values of k and h have to be in order for the ellipse to be centered at (2,3)
If you center the ellipse at (0,0) what will the values of a and b have to be in order for the ellipse to touch the points (-1,0), (1,0) and (0,-2), (0,2).