SOLUTION: determine the center and asymptotes of this hyperbola equation y=x+1/2x-4

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Question 729476: determine the center and asymptotes of this hyperbola equation y=x+1/2x-4
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
y=%28x%2B1%29%2F%282x-4%29

Asymptotes of a hyperbola are the lines that pass through center of the hyperbola and touch the hyperbola.
y=%28x%2B1%29%2F%282x-4%29....since denominator cannot be zero we will find that value of x that makes it equal to zero
2x-4=0...=>...2x=4...=>...x=2...this is x coordinate of the center and asymptote
now find y value for center
y=%28x%2B1%29%2F2%28x-2%29....=>..y=%281%2F2%29%28%28x%2B1%29%2F%28x-2%29%29
so, y coordinate is 1%2F2