document.write( "Question 541721: Problem: 3x^2+12y^2=12
\n" ); document.write( "How do I first write a standard equation of the ellipse and find the coordinates of the center, vertices, co-vertices, and foci? \n" ); document.write( "

Algebra.Com's Answer #354258 by lwsshak3(11628) $\"\"$ $\"About$

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Problem: 3x^2+12y^2=12
\n" ); document.write( "How do I first write a standard equation of the ellipse and find the coordinates of the center, vertices, co-vertices, and foci?
\n" ); document.write( "**
\n" ); document.write( "Standard form of equation for ellipse with horizontal major axis:
\n" ); document.write( "(x-h)^2/a^2+(y-k)^2/b^2=1,a>b, (h,k)=(x,y) coordinates of center
\n" ); document.write( "..
\n" ); document.write( "For given problem:
\n" ); document.write( "3x^2+12y^2=12
\n" ); document.write( "divide by 12
\n" ); document.write( "x^2/4+y^2/1=1
\n" ); document.write( "x^2/4+y^2=1 (standard form of equation for given ellipse)
\n" ); document.write( "..
\n" ); document.write( "Center: (0,0)
\n" ); document.write( "a^2=4
\n" ); document.write( "a=2
\n" ); document.write( "vertices: (0ąa,0)=(0ą2,0)=(-2,0) and (2,0)
\n" ); document.write( "..
\n" ); document.write( "b^2=1
\n" ); document.write( "b=1
\n" ); document.write( "co-vertices: (0,0ąb)=(0,0ą1)=(0,-1) and (0,1)
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2-b^2=4-1=3
\n" ); document.write( "c=√3
\n" ); document.write( "Foci: (0ąc,0)=(0ą√3,0)=(-√3,0) and (√3,0) \n" ); document.write( "

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