What is 14x^2+11y^2-252x-22y+991=0 ?

The solution to 14x^2+11y^2-252x-22y+991=0 is Ellipse with (h,k)=(9,1),a=sqrt(11),b=sqrt(14)

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14x^2+11y^2-252x-22y+991=0

14 x^{2} + 11 y^{2} - 252 x - 22 y + 991 = 0

(h, k) = (9, 1), a = 11, b = 14

Solution steps

14 x^{2} + 11 y^{2} - 252 x - 22 y + 991 = 0

Rewrite

14 x^{2} + 11 y^{2} - 252 x - 22 y + 991 = 0

in the form of the standard ellipse equation

\frac{( x - 9 ) ^{2}}{( 11 ) ^{2}} + \frac{( y - 1 ) ^{2}}{( 14 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (9, 1), a = 11, b = 14

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (9, 1), b = 14, a = 11

\frac{( x + 4 ) ^{2}}{16} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{y ^{2}}{9} = 1 - \frac{x ^{2}}{4}

8 = \frac{1}{2} x^{2} + \frac{1}{4} y^{2}

\frac{( x - 2 ) ^{2}}{25} + \frac{( y - 2 ) ^{2}}{16} = 1

x^{2} = 1 - 4 y^{2}

What is 14x^2+11y^2-252x-22y+991=0 ?
The solution to 14x^2+11y^2-252x-22y+991=0 is Ellipse with (h,k)=(9,1),a=sqrt(11),b=sqrt(14)