Question

If the equation of an ellipse is in standard form and the denominators are equal, then the ellipse is a circle. Is this true or false?

Answer 1

do you know the equation of a circle?

Start with the equation of an ellipse:
\[ \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2 } = 1 \]
make the denominators equal. OK, let b = a so we have
\[ \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{a^2 } = 1 \]
or
\[ \frac{(x-h)^2+(y-k)^2}{a^2} =1 \]
if you multiply both sides by a^2 you get
\[ (x-h)^2+(y-k)^2 = a^2 \]

Answer 2

Thank you!