What is 9x^2+25y^2-18x+200y+184=0 ?

The solution to 9x^2+25y^2-18x+200y+184=0 is Ellipse with (h,k)=(1,-4),a=5,b=3

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9x^2+25y^2-18x+200y+184=0

9 x^{2} + 25 y^{2} - 18 x + 200 y + 184 = 0

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

Solution steps

9 x^{2} + 25 y^{2} - 18 x + 200 y + 184 = 0

Rewrite

9 x^{2} + 25 y^{2} - 18 x + 200 y + 184 = 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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

(x^{2} + 9 x) + (4 y^{2} + 10) = 5

\frac{( x - 3 ) ^{2}}{21} + \frac{( y - 2 ) ^{2}}{25} = 1

\frac{( x - 9 ) ^{2}}{16} + \frac{( y - 11 ) ^{2}}{9} = 1

1 - x^{2} - 5 y^{2} > 0

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{16} = 1

What is 9x^2+25y^2-18x+200y+184=0 ?
The solution to 9x^2+25y^2-18x+200y+184=0 is Ellipse with (h,k)=(1,-4),a=5,b=3