Question 531363
Classify the conic section of the equation 4x2 + 9y2 - 8x - 18y - 19 = 0. 
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4x2 + 9y2 - 8x - 18y - 19 = 0. 
complete the square
4(x^2-2x+1)+9(y^2-2y+1)=19+4+9=32
4(x-1)^2+9(y-1)^2=32
Divide both sides by 32
(x-1)^2/(32/4)+9(y-1)^2/(32/9)=1
(x-1)^2/8+(y-1)^2/(32/9)=1
This an equation of an ellipse with horizontal major axis of the standard form:
(x-h)^2/a^2+(y-k^2)/b^2=1, a>b, with (h,k) being (x,y) coordinates of the center
For given equation:
Center: (1,1)
a^2=8
b^2=32/9