What conic section is drawn by the parametric equations x=csc t and y cot?
A. Parabola
B. Circle
C. Ellipse
D. Hyperbola
2 answers
Hey, you try some now !
If your expression mean:
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
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
1 answer