andreabeat80 andreabeat80
  • 25-07-2020
  • Mathematics
contestada

Find a rectangular equation. X = 3tan t, Y = 2sec t, for in (−π /2 , π /2 )

Respuesta :

Bebong Bebong
  • 25-07-2020

Answer:

Step-by-step explanation:

[tex]x= 3tan(t) \rightarrow tan(t) = \frac{x}{3} \rightarrow tan^2(t) = \frac{x^2}{9}[/tex]

[tex]y= 2sec(t) \rightarrow sec(t) = \frac{y}{2} \rightarrow sec^2(t) = \frac{y^2}{4}[/tex]

[tex]sec^2(t) -tan^2(t) =1[/tex]

[tex]\frac{y^2}{4} -\frac{x^2}{9} =1[/tex]

is the rectangular equation of the parameter functions.

also, it is a hyperbola. The condition [tex]-\pi/2 < t<\pi/2[/tex] limit x from 0 to infinitive

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