Question 620936: Identify the conic section. If it is a parabola, give the vertex. If it is an ellipse or hyperbola, give the center and the foci.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Identify the conic section. If it is a parabola, give the vertex. If it is an ellipse or hyperbola, give the center and the foci.
8x^2-6y^2+48x-24y+0=0
8x^2+48x-6y^2-24y+0=0
complete the square
8(x^2+6x+9)-6(y^2+4y+4)=72-24
8(x+3)^2-6(y+2)^2=48
(x+3)^2/6-(y+2)^2/8=1
This is an equation of a hyperbola with horizontal transverse axis
Its standard form: (x-h)^2/a^2-(y-k)^2/b^2=1, (h,k)=(x,y) coordinates of center
For given hyperbola:
center: (-3,-2)
a^2=6
b^2=8
c^2=a^2+b^2=6+8=14
c=√14≈3.7
foci: (-3±c,-2)=(-3±3.7,-2)=(-6.7,-2) and (0.7,-2)
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