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

Expert Answers

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You should remember the formula of equation of ellipse such that:

`(x/a)^2 + (y/b)^2 = 1`

Notice that a represents the half of major axis and b represents the half of minor axis.

If the lengths of minor and major axis are equal yields:

`a = b`

Substituting r for a and b yields:

`x^2/r^2 + y^2/r^2 = 1`

You need to multiply both sides by `r^2`  such that:

`x^2 + y^2 = r^2`

Notice that `x^2 + y^2 = r^2`  represents the standard form of equation of the circle whose center is at `(0,0)`  and `r`  represents its radius.

Hence, considering the equal lengths of minor and major axis of ellipse, the equation of an ellipse becomes the equation of a circle.

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