Question 724506
1. y(2)+5=4(x+y)
y^2+5=4x+4y
y^2-4y=4x-5
complete the square:
(y^2-4y+4)=4x-5+4
(y-2)^2=4x-1
{{{(y-2)^2=4(x-1/4)}}}
This is an equation of a parabola that opens rightward
Its basic form: {{{(y-k)^2=4p(x-h)}}}, (h,k)=(x,y) coordinates of the vertex
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2. 2x(2)=8x-y(2)
2x^2+8x+y^2=0
complete the square
2(x^2+4x+4)+y^2=0+8
2(x+2)^2+y^2=8
{{{(x+2)^2/4+y^2/8=1}}}
This is an equation of an ellipse with vertical major axis
Its standard form: {{{(x-h)^2/b^2+(y-k)^2/a^2}}}, a>b, (h,k)=(x,y) coordinates of the center
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3. 4(y+1)(y-1)+5x(2)=24
4(y^2-1)+5x^2=24
4y^2-4+5x^2=24
4y^2+5x^2=24+4
4y^2+5x^2=28
{{{y^2/7+x^2/(28/5)=1}}}
This is an equation of an ellipse with horizontal major axis
Its standard form: {{{(x-h)^2/a^2+(y-k)^2/b^2}}}, a>b, (h,k)=(x,y) coordinates of the center