“Ellipse Envelope”的概念、定义、习题解题方法及翻译-数学辞典

单词

Ellipse Envelope

释义

Ellipse Envelope

Consider the family of Ellipses

(1)

for

. The Partial Derivative with respect to

(2)

(3)

Combining (1) and (3) gives the set of equations

(4)


			(5)

where the Discriminant is

(6)

so (5) becomes

(7)

Eliminating

then gives

(8)

which is the equation of the Astroid.If the curve is instead represented parametrically, then

			(9)
			(10)

Solving


	(11)

for

gives

(12)

so substituting this back into (9) and (10) gives

			(13)
			(14)

the parametric equations of the Astroid.

See also Astroid, Ellipse, Envelope

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