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for the equation of the given ellipse 16x^2+4y^2=64. I need help finding the verticies, x or y-intercepts, foci, and how to sketch this also.
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\n" ); document.write( "16x^2+4y^2=64
\n" ); document.write( "divide by 64
\n" ); document.write( "x^2/4+y^2/16=1
\n" ); document.write( "This is an equation for an ellipse with vertical major axis of the standard form:
\n" ); document.write( "(x-h)^2/b^2+(y-k)^2/a^2=1, a>b, (h,k)=(x,y) coordinates of the center
\n" ); document.write( "..
\n" ); document.write( "For given ellipse:
\n" ); document.write( "center: (0,0)
\n" ); document.write( "a^2=16
\n" ); document.write( "a=4
\n" ); document.write( "Vertices: (0, 0±a)=(0,0±4)=(0,-4) and (0,4)
\n" ); document.write( "..
\n" ); document.write( "b^2=4
\n" ); document.write( "b=2
\n" ); document.write( "..
\n" ); document.write( "c^2=a^2-b^2=16-4=12
\n" ); document.write( "c=√12
\n" ); document.write( "Foci: (0, 0±c)=(0,0±√12)=(0,-√12) and (0,√12)
\n" ); document.write( "..
\n" ); document.write( "x-intercepts
\n" ); document.write( "set y=0, then solve for x
\n" ); document.write( "16x^2+4y^2=64
\n" ); document.write( "16x^2=64
\n" ); document.write( "x^2=4
\n" ); document.write( "x=±2
\n" ); document.write( "..
\n" ); document.write( "y-intercepts
\n" ); document.write( "set x=0, then solve for y
\n" ); document.write( "16x^2+4y^2=64
\n" ); document.write( "4y^2=64
\n" ); document.write( "y^2=16
\n" ); document.write( "y=±4
\n" ); document.write( "..
\n" ); document.write( "See graph below as a visual check on answers above:
\n" ); document.write( "y=±(16-4x^2)^.5
\n" ); document.write( "