Question

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

Answer 1

Answer:

Step-by-step explanation:

$x= 3tan(t) \rightarrow tan(t) = \frac{x}{3} \rightarrow tan^2(t) = \frac{x^2}{9}$

$y= 2sec(t) \rightarrow sec(t) = \frac{y}{2} \rightarrow sec^2(t) = \frac{y^2}{4}$

$sec^2(t) -tan^2(t) =1$

$\frac{y^2}{4} -\frac{x^2}{9} =1$

is the rectangular equation of the parameter functions.

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