Question

The pair of parametric equations represents a line, parabola, circle, ellipse, or hyperbola.
Name the type of basic curve that the pair of following equations represent:

x=3cosh(4t)
y=4sinh(4t)

Answer 1

Answer:

Step-by-step explanation:

given that the pair of parametric equations represents a line, parabola, circle, ellipse, or hyperbola.

We are given

$x=3cosh (4t) \\y = 4sinh(4t)$

We know in hyperbolic functions

$cosh^2 (4t) -sinh^2 (4t) =1$

Using this we can find out

$cosh (4t) = \frac{x}{3} \\sinh(4t)=\frac{y}{4}$

Using the identity we can say that

$\frac{x^2}{9} -\frac{y^2}{16} =1$

this is nothing but a hyperbola.

a =3 and b =4