document.write( "Question 854594: I need help \"Identifying the vertices and foci of 4x^2-y^2+32x-14y-85=0\" Thanks! \n" ); document.write( "
Algebra.Com's Answer #514812 by lwsshak3(11628)\"\" \"About 
You can put this solution on YOUR website!
I need help \"Identifying the vertices and foci of
\n" ); document.write( "4x^2-y^2+32x-14y-85=0
\n" ); document.write( "4x^2+32x-y^2-14y=85
\n" ); document.write( "complete the square:
\n" ); document.write( "4(x^2+8x+16)-(y^2+14y+49)=85+64-49
\n" ); document.write( "4(x+4)^2-(y+7)^2=100
\n" ); document.write( "(x+4)^2/25-(y+7)^2/100=1
\n" ); document.write( "This is an equation of a hyperbola with horizontal transverse axis.
\n" ); document.write( "Its standard form of equation: \"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\", (h,k)=coordinates of center
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (-4,-7)
\n" ); document.write( "a^2=25
\n" ); document.write( "a=5
\n" ); document.write( "vertices=(-4±a,-7)=(-4±5,-7)=(-9,-7) and (1,-7)
\n" ); document.write( "b^2=100
\n" ); document.write( "b=10
\n" ); document.write( "c^2=a^2+b^2=25+100=125
\n" ); document.write( "c=√125≈11.2
\n" ); document.write( "foci=(-4±c,-7)=(-4±11.2,-7)=(-15.2,-7) and (7.2,-7)
\n" ); document.write( " \n" ); document.write( "
\n" );