SOLUTION: 1.) 4y2-x2+8y+4x-4=0 Please include a) standard equation form b) opens up and down, or left and right c) Vertex e) Determine A and B f) Graph (asymptotes, rectangular box)

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: 1.) 4y2-x2+8y+4x-4=0 Please include a) standard equation form b) opens up and down, or left and right c) Vertex e) Determine A and B f) Graph (asymptotes, rectangular box)      Log On


   

Question 43399This question is from textbook College Algebra
: 1.) 4y2-x2+8y+4x-4=0
Please include
a) standard equation form
b) opens up and down, or left and right
c) Vertex
e) Determine A and B
f) Graph (asymptotes, rectangular box)




This question is from textbook College Algebra

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
4y%5E2+-+x%5E2+%2B+8y+%2B+4x+-+4+=+0
4y%5E2+%2B+8y+-+x%5E2+%2B+4x+=+4
%284y%5E2+%2B+8y%29+-+%28x%5E2+%2B+4x%29+=+4
4%28y+%2B+1%29%5E2+-+%28x+%2B+2%29%5E2+=+4+%2B+4+%2B+4
%28%28y+%2B+1%29%5E2%29%2F2+-+%28%28x+%2B+2%29%5E2%29%2F8+=+1
Vertex: (-2,-1)
Transverse Axis: vertical (opens up and down)
A = sqrt%282%29
B = sqrt%288%29
Asymptotes:
Slope(M) = +-A/B = +-sqrt%282%29%2Fsqrt%288%29 = +-sqrt%282%29%2F%282%2Asqrt%282%29%29 = +-1%2F2
y+-+y1+=+M%28x+-+x1%29
y+%2B+1+=+0.5%28x+%2B+2%29 and y+%2B+1+=+-0.5%28x+%2B+2%29
y+%2B+1+=+0.5x+%2B+1 and y+%2B+1+=+-0.5x+-+1
y+=+0.5x and y+=+-0.5x+-+2