Question 606785
Actually, you didn't give me an equation, so
I can't give you an equation. You need an "="
sign somewhere, so I'll assume you have
{{{ y^2 - x^2 + 2y - 14x - 57 = 0 }}}
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Add {{{ 57 }}} to both sides
{{{ y^2 - x^2 + 2y - 14x = 57 }}}
Rearrange the terms on the left
{{{ y^2 + 2y - x^2 - 14x = 57 }}}
Complete the square for the y terms and the x terms
{{{ ( y^2 + 2y + (2/2)^2 ) - ( x^2 + 14x + (14/2)^2 ) = 57 + (2/2)^2 - (14/2)^2 }}}
{{{ ( y^2 + 2y + 1 ) - ( x^2 + 14x + 49 ) = 57 + 1 - 49 }}}
{{{ ( y + 1 )^2 - ( x + 7 )^2 = 9 }}}
Divide both sides by {{{ 9 }}}
{{{ ( y + 1 )^2/ 3^2 - ( x + 7 )^2/ 3^2 = 1 }}}
This is a hyperbola with center at (-7,-1)