Monday, May 26, 2014

College Algebra, Chapter 8, Review Exercises, Section Review Exercises, Problem 38

Identify the type of curve which is represented by the equation 2x2+4=4x+y2
Find the foci and vertices(if any), and sketch the graph

y22(x22x)=4Factor and group termsy22(x22x+1)=42Complete the square; Add (22)2=1 on the left and subtract 2 from the righty22(x1)2=2Perfect squarey22(x1)2=1Divide by 2


The equation is hyperbola that has the form (yk)2a2(xh)2b2=1 with center at (h,k) and vertical transverse axis.
The graph of the shifted hyperbola is obtained from the graph of y22x2=1 by shifting it 1 unit to the right. This gives us a
a2=2 and b2=1, so a=2,b=1 and c=a2+b2=2+1=3. Then, by applying transformation

center (h,k)(1,0)vertices (0,a)(0,2)(0+1,2)=(1,2)(0,a)(0,2)(0+1,2)=(1,2)foci (0,c)(0,3)(0+1,3)=(1,3)(0,c)(0,3)(0+1,3)=(1,3)

Then, the graph is

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