document.write( "Question 786519: How do i find the center, vertices, co-vertices and foci of these equations?
\n" ); document.write( "1. 25x2 + 9y2 = 225\r
\n" ); document.write( "\n" ); document.write( "2. 49x2 + y2 = 49\r
\n" ); document.write( "\n" ); document.write( "3. x2 - 2x + 9y2 - 8 = 0\r
\n" ); document.write( "\n" ); document.write( "4. x2 + 4y2 - 18x -8y + 81 = 0 \n" ); document.write( "
Algebra.Com's Answer #478034 by lwsshak3(11628)\"\" \"About 
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How do i find the center, vertices, co-vertices and foci of these equations?
\n" ); document.write( "**
\n" ); document.write( "Standard form of equation for ellipses:
\n" ); document.write( "1)With horizontal major axis: \"%28x-h%29%5E2%2Fa%5E2%2B%28y-k%29%5E2%2Fb%5E2=1\", a>b, (h,k)=(x,y) coordinates of the center.
\n" ); document.write( "2)With vertical major axis: \"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2=1\", a>b, (h,k)=(x,y) coordinates of the center.
\n" ); document.write( "..
\n" ); document.write( "1. 25x2 + 9y2 = 225
\n" ); document.write( "divide by 225
\n" ); document.write( "x^2/9+y^2/25=1
\n" ); document.write( "ellipse has vertical major axis
\n" ); document.write( "center: (0,0)
\n" ); document.write( "a^2=25
\n" ); document.write( "a=√25=5
\n" ); document.write( "vertices: (0,±5)
\n" ); document.write( "b^2=9
\n" ); document.write( "b=√9=3
\n" ); document.write( "co-vertices:(±3,0)
\n" ); document.write( "c^2=a^2-b^2=25-9=16
\n" ); document.write( "c=√16=4
\n" ); document.write( "foci:(0,±4)
\n" ); document.write( "..
\n" ); document.write( "2. 49x2 + y2 = 49
\n" ); document.write( "divide by 49
\n" ); document.write( "x^2+y^2/49=1
\n" ); document.write( "ellipse has vertical major axis
\n" ); document.write( "center: (0,0)
\n" ); document.write( "a^2=49
\n" ); document.write( "a=√49=7
\n" ); document.write( "vertices: (0,±7)
\n" ); document.write( "b^2=1
\n" ); document.write( "b=1
\n" ); document.write( "co-vertices:(±1,0)
\n" ); document.write( "c^2=a^2-b^2=49-1=48
\n" ); document.write( "c=√48
\n" ); document.write( "foci:(0,±√48)
\n" ); document.write( "..
\n" ); document.write( "3. x2 - 2x + 9y2 - 8 = 0
\n" ); document.write( "complete the square
\n" ); document.write( "(x^2-2x+1)+9y^2=8+1
\n" ); document.write( "(x-1)^2+9y^2=9
\n" ); document.write( "divide by 9
\n" ); document.write( "x^2/9+y^2=1
\n" ); document.write( "ellipse has horizontal major axis
\n" ); document.write( "center: (1,0)
\n" ); document.write( "a^2=9
\n" ); document.write( "a=√9=3
\n" ); document.write( "vertices: (-2,0),(4,0)
\n" ); document.write( "b^2=1
\n" ); document.write( "b=1
\n" ); document.write( "co-vertices:(0,±1)
\n" ); document.write( "c^2=a^2-b^2=9-1=8
\n" ); document.write( "c=√8
\n" ); document.write( "foci:(1-√8,0),(1+√8,0)
\n" ); document.write( "..
\n" ); document.write( "4. x2 + 4y2 - 18x -8y + 81 = 0
\n" ); document.write( "x^2-18x+4y^2-8y=-81
\n" ); document.write( "complete the square:
\n" ); document.write( "(x^2-18x+81)+4(y^2-2y+1)=-81+81+4
\n" ); document.write( "(x-9)^2+4(y-1)^2=4
\n" ); document.write( "divide by 4
\n" ); document.write( "(x-9)^2/4+(y-1)^2=1
\n" ); document.write( "ellipse has horizontal major axis
\n" ); document.write( "center: (9,1)
\n" ); document.write( "a^2=4
\n" ); document.write( "a=√4=2
\n" ); document.write( "vertices: (7,1),(11,1)
\n" ); document.write( "b^2=1
\n" ); document.write( "b=1
\n" ); document.write( "co-vertices:(9,0),(9,2)
\n" ); document.write( "c^2=a^2-b^2=4-1=3
\n" ); document.write( "c=√3
\n" ); document.write( "foci:(9-√3,1),(9+√3,1)
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