# SOLUTION: determine the center, vertices, foci for the following ellipse.18x2+y2_108x+4y+148?

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 Click here to see ALL problems on Quadratic-relations-and-conic-sections Question 430265: determine the center, vertices, foci for the following ellipse.18x2+y2_108x+4y+148?Answer by lwsshak3(6478)   (Show Source): You can put this solution on YOUR website!determine the center, vertices, foci for the following ellipse.18x2+y2_108x+4y+148? .. Standard form of ellipse for horizontal major axis: (x-h)^2/a^2+(y-k)^2/b^2=1 (a>b) Standard form of ellipse for vertical major axis: (y-k)^2/a^2+(x-h)^2/b^2=1 (a>b) In both forms, (h,k) represent the (x,y) coordinates of the center. .. 18x2+y2_108x+4y+148 completing the squares: 18(x^2-6x+9)+(y^2+4y+4)=-148+162+4=18 divide by 18 (x-3)^2/1+(y+2)^2/18=1 change positions (y+2)^2/18+(x-3)^2/1=1 This is an ellipse with a vertical major axis(second form described above) .. center: (3,-2) a^2=18 a=sqrt(18)=4.24.. b=1 b^2=1 c^2=a^2-b^2=18-1=17 c=sqrt(17)=4.12.. Vertices are on the major axis on the line,x=3, -2+-4.24 or (3,2.24) and (3,-6.24) Similarly, foci are on the major axis,-2+-4.12 or (3,2.12) and (3,-6.12) Graph below can visually confirm the answers obtained. .. y=+-((1-(x-3)^2)18)^.5-2 ..