# Pre-Calculus Help?

What conic section is drawn by the parametric equations x=csc t and y cot?

A. Parabola

B. Circle

C. Ellipse

D. Hyperbola

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1. Hey, you try some now !

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x = csc t and y = cot t

then:

x = csc t

x = 1 / sin t

sin t = 1 / x

y = cot t = cos t / sin t = ± √ ( 1 - sin² t ) / sin t = ± √ ( 1 - sin² t ) ∙ 1 / sin t =

± √ ( 1 - sin² t ) ∙ csc t = ± √ [ 1 - ( 1 / x )² ] ∙ x = ± √ ( x² / x² - 1 / x² ) ∙ x =

± √ [ ( x² - 1 ) / x² ] ∙ x =± [ √ ( x² - 1 ) / √ x² ] ∙ x =

± [ √ ( x² - 1 ) / x ] ∙ x = ± √ ( x² - 1 )

y = ± √ ( x² - 1 )
hyperbola

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