What is 9x^2+4y^2+18x-40y+73=0 ?

The solution to 9x^2+4y^2+18x-40y+73=0 is Ellipse with (h,k)=(-1,5),a=2,b=3

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9x^2+4y^2+18x-40y+73=0

9 x^{2} + 4 y^{2} + 18 x - 40 y + 73 = 0

(h, k) = (- 1, 5), a = 2, b = 3

Solution steps

9 x^{2} + 4 y^{2} + 18 x - 40 y + 73 = 0

Rewrite

9 x^{2} + 4 y^{2} + 18 x - 40 y + 73 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 5), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 5), b = 3, a = 2

\frac{( x + 8 ) ^{2}}{64} + \frac{( y - 11 ) ^{2}}{36} = 1

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

\frac{x ^{2}}{2 5} + \frac{36 - 12 y + y ^{2}}{6} = 1

49 x^{2} + 100 y^{2} + 882 x - 1400 y + 3969 = 0

x^{2} + 4 y^{2} = 4 x

What is 9x^2+4y^2+18x-40y+73=0 ?
The solution to 9x^2+4y^2+18x-40y+73=0 is Ellipse with (h,k)=(-1,5),a=2,b=3