Question 1010714
{{{5x^2-5y^2+40x-20y+35=0}}}
{{{x^2-y^2+8x-4y+7=0}}}
{{{x^2+8x-y^2-4y=-7}}}
Complete the squares as described , <a href="http://www.algebra.com/my/Completing-the-Square-to-Solve-General-Quadratic-Equation.lesson?content_action=show_dev">...includes how to complete the square</a>
{{{x^2+8x+16-(y^2-4y+2)=-7+16-2}}}
{{{(x+4)^2-(y-2)^2=7}}}
{{{highlight((x+4)^2/7-(y-2)^2/7=1)}}}


HYPERBOLA
Center  (-4,2)


If c is the distance from a focus to the center, then  using {{{a^2=7}}} and {{{b^2=7}}},
{{{c^2=b^2+a^2}}}
{{{c^2=7+7}}}
{{{c^2=14}}}
{{{c=sqrt(14)}}}
Being a horizontal hyperbola, vertices on the x-axis, the foci are (-4-sqrt(14),  2) and (-4+sqrt(14),  2).