SOLUTION: Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci. y^2/16 - x^2/9 = 1

Algebra.Com
Question 616682: Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci.
y^2/16 - x^2/9 = 1
Found 2 solutions by lwsshak3, ewatrrr:
Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci.
y^2/16 - x^2/9 = 1
**
Equation is that of a hyperbola with vertical transverse axis.
Its standard form: (y-k)^2/a^2-(x-h)^2/b^2=1, (h,k)=(x,y) coordinates of the center
For given equation:
center: (0,0)
a^2=16
a=√16=4
vertices: (0, 0±a)=(0,0±4)=(0,-4) and (0,4)
..
b^2=9
b=√9=3
..
c^2=a^2+b^2=16+9=25
c=√25=5
foci:(0, 0±c)=(0,0±5)=(0,-5) and (0,5)
...
slopes of asymptotes with vertical transverse axis=±a/b=±4/3
asymptotes are straight lines which intersect at the center.
equation:y=mx+b, m=slope, b=y-intercept
y-intercept=0, since asymptotes go thru the origin(0,0)
equation of asymptote with negative slope: y=-4x/3
equation of asymptote with positive slope: y=4x/3
..
see graph below:
y=±(16+16x^2/9)^.5


Answer by ewatrrr(24785)   (Show Source): You can put this solution on YOUR website!
 

Hi,

  or 

center, (0,0)

asymptotes, y = ± 4/3x

vertices, (0,-4), (0,4)

and foc(0,-5),(0,5)   ||Note: = 5



 

RELATED QUESTIONS


Sketch the hyperbolas. Identify the center, asymptotes, vertices, and foci.
(x-3)^2/9 -... (answered by lwsshak3)

(x-3)^(2)/(9)-(y+5)^(2)/(16)=1

Identify the curve; find the center,asymptotes,... (answered by lwsshak3)

it says, "Identify the curve and find the characteristics listed. then sketch the curve."
 (answered by lwsshak3)

y^(2)/(16)-x^(2)/(9)=1

Identify the curve, find the center,asymptotes, foci; then... (answered by lwsshak3)

Hyperbolas: 
Graph each hyperbola. Identify the verices, foci, and asymptotes

X^2/4 -  (answered by lwsshak3)

it says, "Identify the curve and find the characteristics listed. then sketch the curve."
 (answered by ewatrrr)

74.) Sketch the ellipse. Identify the center, vertices, and foci.... (answered by lwsshak3)

Identify the center, vertices, foci, transverse, asymptotes, domain, and range for the... (answered by ewatrrr)

Find the center, vertices, foci, and asymptotes of the hyperbola.

{{{(x+4)^2/16 -... (answered by lwsshak3)