Question 555133: 4x^2+9y^2-8x-18y-23=0
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 4x^2+9y^2-8x-18y-23=0
complete the square
4(x^2-2x+1)+9(y^2-2y+1)=23+4+9
4(x-1)^2+9(y-1)^2=36
divide by 36
(x-1)^2/9+(y-1)^2/4=1
This is an equation of an ellipse with horizontal major axis of the standard form:
(x-h)^2/a^2+(y-k)^2/b^2=1, a>b, (h,k) being the (x,y) coordinates of the center.
For given equation:
center(1,1)
a^2=9
a=√9=3
vertices: (1±a,1)=(1±3,1)=(-2,1) and (4,1)
b^2=4
b=√4=2
co-vertices: (1,1±b)=(1,1±2)=(1,-1) and (1,3)
you now have the information you need to graph the ellipse
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