document.write( "Question 767746: 4x^2+y^2-48x-4y+48=0 find center C, length of major axis, length of minor axis, distance from C to foci? \n" ); document.write( "

Algebra.Com's Answer #467815 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
4x^2+y^2-48x-4y+48=0 find center C, length of major axis, length of minor axis, distance from C to foci?
\n" ); document.write( "***
\n" ); document.write( "4x^2+y^2-48x-4y+48=0
\n" ); document.write( "complete the square:
\n" ); document.write( "4x^2-48x+y^2-4y+48=0
\n" ); document.write( "4(x^2-12x+36)+(y^2-4y+4)=-48+144+4
\n" ); document.write( "4(x-6)^2+(y-2)^2=100
\n" ); document.write( "(x-6)^2/25+(y-2)^2/100=1
\n" ); document.write( "This is an equation of an ellipse with vertical major axis
\n" ); document.write( "Its standard form: $\"%28x-h%29%5E2%2Fb%5E2%2B%28y-k%29%5E2%2Fa%5E2\"$ , a>b, (h,k)=(x,y) coordinates of the center
\n" ); document.write( "For given ellipse:
\n" ); document.write( "center: (6,2)
\n" ); document.write( "a^2=100
\n" ); document.write( "a=√100=10
\n" ); document.write( "length of major axis=2a=20
\n" ); document.write( "b^2=25
\n" ); document.write( "b=√25=5
\n" ); document.write( "length of minor axis=2b=10
\n" ); document.write( "c^2=a^2-b^2=100-25=75
\n" ); document.write( "c=√75
\n" ); document.write( "distance from center to foci=√75≈8.66 \n" ); document.write( "

\n" );