What is 9x^2+5y^2-18x-40y+44=0 ?

The solution to 9x^2+5y^2-18x-40y+44=0 is Ellipse with (h,k)=(1,4),a=sqrt(5),b=3

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9x^2+5y^2-18x-40y+44=0

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

(h, k) = (1, 4), a = 5, b = 3

Solution steps

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

Rewrite

9 x^{2} + 5 y^{2} - 18 x - 40 y + 44 = 0

in the form of the standard ellipse equation

\frac{( x - 1 ) ^{2}}{( 5 ) ^{2}} + \frac{( y - 4 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, 4), a = 5, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, 4), b = 3, a = 5

\frac{( x - 3 ) ^{2}}{9} + \frac{( y - 4 ) ^{2}}{16} = 1

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

\frac{( y + 3 ) ^{2}}{25} + \frac{( x + 4 ) ^{2}}{16} = 1

3 x^{2} + 4 y^{2} - 16 = 0

x^{2} + 4 x + 2 y^{2} + 6 y + 1 = 0

What is 9x^2+5y^2-18x-40y+44=0 ?
The solution to 9x^2+5y^2-18x-40y+44=0 is Ellipse with (h,k)=(1,4),a=sqrt(5),b=3