Question 144041
4x^2+9y^2-16x-18y=11 
this is the expanded equation, so how do i find the STANDARD form of 
this equation?? and how do i find the coordinates of 4 VERTICES??? 
including major and minor axis??? 
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1st: complete the square separately on the x and on the y terms to get:

[4x^2-16x] +[9y^2-18y] = 11

[4(x^2-4x+4)] + [9[y^2-2y+1)] = 11+4*4 + 9*1 = 36

Divide thru by 36 to get:
(x-2)^2/9 + (y-1)^2/4 = 1

This is the standard form of an ellipse:

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Center: (h,k) = (2,1)
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Semi-major axis = sqrt9 = 3
Semi-minor axis = sqrt4 = 2
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Vertices on the major axis: (2+3,1) and (2-3,1)
vertices on the minor axis: (2,1+2) and (2,1-2)
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Cheers,
Stan H.