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
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