## anonymous one year ago 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?

1. phi

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 $(x-h)^2+(y-k)^2 = a^2$

2. anonymous

Thank you!