Question 665077
ellipse: {{{4x^2 + 24x + y^2 + 8y = -36}}}


{{{4x^2 + 24x + y^2 + 8y +36=0}}}



{{{(4x^2 + 24x +36) + y^2 + 8y=0}}}


{{{4(x^2 + 6x +9) + y^2 + 8y=0}}}


{{{4(x+3)^2 + (y^2 + 8y+16)-16=0}}}


{{{4(x+3)^2 + (y +4)^2=16}}}


{{{4(x+3)^2/16 + (y +4)^2/16=16/16}}}


{{{(x+3)^2/4 + (y +4)^2/16=1}}}........{{{a^2=4}}} and {{{b^2=16}}}

2.

To convert an equation from standard form to vertex form it is sometimes necessary to be comfortable completing the square.

The vertex form of a parabola's equation is generally expressed as :

{{{y= a(x-h)^2+k}}} 


{{{x^2 + 12x + 36 = 4y - 28}}}

{{{(x +6)^2 = 4y - 28}}}

{{{(x +6)^2+28 = 4y }}}

{{{(x +6)^2/4+28/4 = y }}}

{{{y=(x +6)^2/4+7 }}}


{{{y=(1/4)(x +6)^2+7 }}}