Show, using algebra, that the formula  for a circle  is a special case of the formula  for an ellipse.

Expert Answers

An illustration of the letter 'A' in a speech bubbles

The formula for a circle is `(x-h)^2+(y-k)^2=r^2` where the center of the circle is at (h,k) and the radius is r.

The formula for an ellipse is `((x-h)^2)/a^2+((y-k)^2)/b^2=1` where (h.k) is the center of the ellipse and a and b are the semi-major and simi-minor axes.

Assume we have an ellipse centered at (h,k) whose major and minor axis have equal length. This describes a circle centered at (h,k).

Then `((x-h)^2)/a^2+((y-k)^2)/a^2=1`

`(x-h)^2+(y-k)^2=a^2` by multiplying through by `a^2`

which is the formula for a circle centered at (h,k). Thus the formula for a circle is a special case of the formula for an ellipse.

 

Approved by eNotes Editorial Team
Soaring plane image

We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

  • 30,000+ book summaries
  • 20% study tools discount
  • Ad-free content
  • PDF downloads
  • 300,000+ answers
  • 5-star customer support
Start your 48-Hour Free Trial