Determine the set of parametric equations for the hyperbola with vertices at ( 5 , 0 ) (5, 0) ( 5 , 0 ) and ( − 5 , 0 ) (-5, 0) ( − 5 , 0 ) , and foci at ( 8 , 0 ) (8, 0) ( 8 , 0 ) and ( − 8 , 0 ) (-8, 0) ( − 8 , 0 ) .

x = 5 sec ⁡ ( t ) , y = 39 tan ⁡ ( t ) x=5\sec(t),y=\sqrt{39}\tan(t) x = 5 sec ( t ) , y = 39 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> tan ( t )

x = 39 sec ⁡ ( t ) , y = 5 tan ⁡ ( t ) x=\sqrt{39}\sec(t),y=5\tan(t) x = 39 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> sec ( t ) , y = 5 tan ( t )

x = 8 sec ⁡ ( t ) , y = 5 tan ⁡ ( t ) x = 8\sec(t), y = 5\tan(t) x = 8 sec ( t ) , y = 5 tan ( t )

x = 5 tan ⁡ ( t ) , y = 39 sec ⁡ ( t ) x=5\tan(t),y=\sqrt{39}\sec(t) x = 5 tan ( t ) , y = 39 <path d="M95,702 c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14 c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54 c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10 s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429 c69,-144,104.5,-217.7,106.5,-221 l0 -0 c5.3,-9.3,12,-14,20,-14 H400000v40H845.2724 s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7 c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47z M834 80h400000v40h-400000z"> sec ( t )

10. Parametric Equations

10. Parametric Equations / Writing Parametric Equations / Problem 2

Determine the set of parametric equations for the hyperbola with vertices at $(5, 0)$ and $(-5, 0)$ , and foci at $(8, 0)$ and $(-8, 0)$ .

$x=5\sec(t),y=\sqrt{39}\tan(t)$

$x=\sqrt{39}\sec(t),y=5\tan(t)$

$x = 8\sec(t), y = 5\tan(t)$

$x=5\tan(t),y=\sqrt{39}\sec(t)$

Learn this concept

Determine the set of parametric equations for the hyperbola with vertices at ﻿(5,0)(5, 0)(5,0)﻿ and ﻿(−5,0)(-5, 0)(−5,0)﻿, and foci at ﻿(8,0)(8, 0)(8,0)﻿ and ﻿(−8,0)(-8, 0)(−8,0)﻿.

Determine the set of parametric equations for the hyperbola with vertices at $(5, 0)$ and $(-5, 0)$ , and foci at $(8, 0)$ and $(-8, 0)$ .