You can put this solution on YOUR website! complete the square and graph conics
1) 25x^2+25y^2=16+24y+9y^2
16y^2-24y+25x^2=16
16(y^2-1.5y+.5625)+25x^2=16+9
16(y-.75)^2+25x^2=25
x^2+(y-.75)^2/(25/16)=1
This is 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 center.
For given equation:
center:(0,.75)
see graph below:
y=±(25/16-25x^2/16)^.5-.75
...
2) x^2+y^2=x^2-4x+4
y^2=-4x+4
y^2=-4(x-1)
This is an equation of a parabola that opens leftwards.
Its standard form: (y-k)^2=4p(x-h), (h,k)=(x,y) coordinates of vertex
see graph below:
y=±(-4x+4)^.5
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