Question 665077
it says, "Complete the square and write each equation in the standard form?"
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standard form of equation for an ellipse with vertical major axis: {{{(x-h)^2/b^2+(y-k)^2/a^2}}}, a>b, (h,k)=(x,y) coordinates of the center.
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ellipse: 4x^2 + 24x + y^2 + 8y = -36
4(x^2+6x+9)+(y^2+8y+6) = -36+36+6
4(x+3)^2+(y+3)^2=6
{{{(x+3)^2/(3/2)+(y+3)^2/6=1}}}
This is an equation of and ellipse with vertical major axis and center at (-3,-3)
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standard form of equation for a parabola:{{{y=A(x-h)^2+k}}}, (h,k)=(x,y) coordinates of the vertex, A=multiplier that affects the slope or narrowness of the curve. For A>0, parabola opens upwards, and for A<0 parabola opens downwards
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parabola: x^2 + 12x + 36 = 4y - 28
4y=x^2+12x+36+28
4y=x^2+12x+64  
4y=(x^2+12x+36)+64-36
4y=(x+6)^2+28
y=(1/4)(x+6)^2+7
{{{y=(1/4)(x+6)^2+7}}}
This is an equation of a parabola that opens upwards with vertex at (-6,7)