SOLUTION: Sketch the graph of the hyperbola y^2/25- x^2/4= 1. Draw the fundamental rectangle. Find the equations of the asymptotes and label the asymptotes on your graph.

Question 88789: Sketch the graph of the hyperbola y^2/25- x^2/4= 1. Draw the fundamental rectangle. Find the equations of the asymptotes and label the asymptotes on your graph.
Found 2 solutions by venugopalramana, Nate:
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
Sketch the graph of the hyperbola y^2/25- x^2/4= 1. Draw the fundamental rectangle. Find the equations of the asymptotes and label the asymptotes on your graph
STD. EQN IS
(Y-K)^2/B^2 - (X-H)^2/A^2 =1
COMPARING H=K=0....A=2......B=5
CENTER IS (H,K)=(0,0)
TRANSVERSE AXIS IS X=H=0
LENGTH OF TRANSVERSE AXIS = 2B=10
CONJUGATE AXIS IS Y=K=0
LENGTH OF CONJUGATE AXIS = 2A =4
VERTICES ARE [H,K+-B]=(0,5) AND (0,5)
USE THIS DATA TO SKETCH.IF NECESSARY GIVE SOME VALUES TO X AND FIND Y AND PLOT
CURVES ARE SYMMETRIC ABOUT AXES
ASYMPTOTES ARE GIVEN BY
Y^2/25 - X^/4 = 0
[(Y/5)+(X/4)][(Y/5)-(X/4)]=0
Y/5 = X/4
AND Y/5 = -X/4
GRAPH IS SHOWN BELOW

Answer by Nate(3500) (Show Source): You can put this solution on YOUR website!
Asymptotes: y = 2.5x and y = -2.5x

~ Vertical Hyperbola
~ 2a units vertical ~> 10 units
~ 2b units horizontal ~> 4 units
~ Centre: (0,0)
Points for fundamental rectangle: (2,5), (-2,5), (2,-5), (-2,-5)
~ Asymptotes:
m = (5 - 0)/(2 - 0) = 2.5 and m = (-5 - 0)/(2 - 0) = -2.5
y = 2.5(x - 0) + 0 and y = -2.5(x - 0) + 0
y = 2.5x and y = -2.5

RELATED QUESTIONS
Find the vertices,foci,and asymptotes of the hyperbola. Then sketch the graph... (answered by lwsshak3)
Use vertices and asymptotes to graph the hyperbola. Find the equations of the asymptotes? (answered by KMST)
y^2/36-x^2/4=1. find the coordinates of the vertices and foci and the equations of the... (answered by lwsshak3)
Use vertices and asymptotes to graph each hyperbola. Locate the foci and find the... (answered by lwsshak3)
Find the four corners of the fundamental rectangle of the hyperbola: (x^2/81)-(x^2/36)=1 (answered by Edwin McCravy)
Find the vertices, foci, and the equations of the asymptotes of the hyperbola... (answered by MathLover1)
Find the coordinates of the vertices and foci and the equations of the asymptotes for the (answered by lwsshak3)
Find the center, the vertices, the foci, and the asymptotes of the hyperbola. Then draw... (answered by lynnlo)
The equation of a hyperbola is given by y^2/25 - (x-6)^2/144 = 1. a. Identify the... (answered by lwsshak3)