document.write( "Question 721008: write the equation of a hyperbola in standard form whose center is (-2, -4), a focus at (-2, 6), and eccentricity of 5/4. \n" ); document.write( "

Algebra.Com's Answer #442227 by lwsshak3(11628) $\"\"$ $\"About$

You can put this solution on YOUR website!
write the equation of a hyperbola in standard form whose center is (-2, -4), a focus at (-2, 6), and eccentricity of 5/4.
\n" ); document.write( "***
\n" ); document.write( "Given hyperbola has a vertical transverse axis. (From given center and focus data, y-coordinates change but x-coordinates do not.)
\n" ); document.write( "Its standard form of equation: $\"%28y-k%29%5E2%2Fa%5E2-%28x-k%29%5E2%2Fb%5E2=1\"$ , (h,k)=(x,y) coordinates of center,
\n" ); document.write( "For given hyperbola:
\n" ); document.write( "center: (-2,-4)
\n" ); document.write( "c=10 (-4 to 6) (distance from center to focus on vertical transverse axis)
\n" ); document.write( "c^2=100
\n" ); document.write( "eccentricity=5/4=c/a
\n" ); document.write( "a=4c/5=40/5=9
\n" ); document.write( "a^2=81
\n" ); document.write( "c^2=a^2+b^2
\n" ); document.write( "b^2=c^2-a^2=100-81=19
\n" ); document.write( "Equation of given hyperbola:
\n" ); document.write( " $\"%28y%2B4%29%5E2%2F81-%28x%2B2%29%5E2%2F19=1\"$ \n" ); document.write( "

\n" );