kiyondinewton02
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Sagot :

Trancescient

Step-by-step explanation:

Given:

[tex]r^2(b^2\cos^2{\theta} + a^2\sin^2{\theta}) = a^2b^2[/tex]

or

[tex]b^2(r^2\cos^2{\theta}) + a^2(r^2\sin^2{\theta}) = a^2b^2[/tex]

Let [tex]x = r\cos{\theta}[/tex] and [tex]y = \sin{\theta}.[/tex] Substituting these into our given equation, we get

[tex]b^2x^2 + a^2y^2 = a^2b^2[/tex]

Dividing both sides by [tex]a^2b^2,[/tex] we get

[tex]\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1[/tex]

which we recognize as an equation for an ellipse.

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