SOLUTION: Write an equation of the ellipse in standard form. Then identify the major and minor axes. 7x^2+3y^2-28x-12y+4=-19

Question 600682: Write an equation of the ellipse in standard form. Then identify the major and minor axes.
7x^2+3y^2-28x-12y+4=-19
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Write an equation of the ellipse in standard form. Then identify the major and minor axes.
7x^2+3y^2-28x-12y+4=-19
complete the squares
7(x^2-4x+4)+3(y^2-4y+4)=-19-4+28+12
7(x-2)^2+3(y-2)^2=17
divide by 17
(x-2)^2/(17/7)+(y-2)^2/(17/3)=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=1, a>b, (h,k)=(x,y) coordinates of center
For given equation:(x-2)^2/(17/7)+(y-2)^2/(17/3)=1
center: (2,2)
a^2=17/3
a=√(17/3)
length of vertical major axis=2a=2*√(17/3)≈4.76
..
b^2=17/7
b=√(17/7)
length of minor axis=2b=2*√(17/7)≈3.12

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