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