SOLUTION: it says, "Complete the square and write each equation in the standard form?" ellipse: 4x^2 + 24x + y^2 + 8y = -36 parabola: x^2 + 12x + 36 = 4y

SOLUTION: it says, "Complete the square and write each equation in the standard form?" ellipse: 4x^2 + 24x + y^2 + 8y = -36 parabola: x^2 + 12x + 36 = 4y - 28 please help!

Question 665077: it says, "Complete the square and write each equation in the standard form?"
ellipse: 4x^2 + 24x + y^2 + 8y = -36
parabola: x^2 + 12x + 36 = 4y - 28
please help!
Found 2 solutions by MathLover1, lwsshak3:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
ellipse:

........ and
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 :

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
it says, "Complete the square and write each equation in the standard form?"
..
standard form of equation for an ellipse with vertical major axis: , a>b, (h,k)=(x,y) coordinates of the center.
..
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

This is an equation of and ellipse with vertical major axis and center at (-3,-3)
..
standard form of equation for a parabola:, (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
..
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

This is an equation of a parabola that opens upwards with vertex at (-6,7)
RELATED QUESTIONS
it says, "Write each equation in standard form?" ellipse: 96(x+6)^2 +24(y-4)^2 = 96... (answered by ewatrrr)
2.Classify the conic section and write its equation in standard form. Ellipse, Parabola,... (answered by ewatrrr)
How do you convert the equation 4x^2+25y^2-24x+100y+36=0 to its standard form by... (answered by KMST)
Write each equation in standard form. state whether the graph of the equation is a... (answered by Fombitz)
Identify the vertices, foci, and slope of the asymptotes for the hyperbola x^2/25 -... (answered by lwsshak3)
we are doing conics in algebra and we have to put these equation into the standard form... (answered by ewatrrr)
Classify the conic section and write its equation in standard form. 1) 4x^2 + y^2 -... (answered by lynnlo)
Write each equation in standard form. State whether the graph of the equation is a... (answered by lwsshak3)
write the equation y^2 - 8y - 8x = 8 in standard form.... (answered by lwsshak3)