You can put this solution on YOUR website! what is the graphic equation of? 4x2 + 9y2 - 16x -126y + 421
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To find out which conic equation this is, you need to complete the square.
4x2+9y2-16x-126y+421
=4x^2-16x+9y^2-126y=-421
=4(x^2-4x+4)+9(y^2-14y+49)=-421+16+441=36
=4(x-2)^2+9(y-7)^2=36
divide by 36
=(x-2)^2/9+(y-7)^2/4=1
Standard form of an ellipse:(x-h)^2/a^2+(y-k)^2/b=1, with (h,k) being the (x,y) coordinates of the center. Length of major axis=2a. Length of minor axis=2b. Length of vertices=sqrt(a^2-b^2)
From this equation, you should see that the equation is an ellipse with center at (2,7) and a horizontal major axis.
See the graph below:
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y=7+-(4-4(x-2)^2/9)^.5
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