What is 9x^2+25y^2-18x-50y-191=0 ?

The solution to 9x^2+25y^2-18x-50y-191=0 is Ellipse with (h,k)=(1,1),a=5,b=3

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9x^2+25y^2-18x-50y-191=0

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

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

Solution steps

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

Rewrite

9 x^{2} + 25 y^{2} - 18 x - 50 y - 191 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

3 x^{2} + 3 y^{2} - 6 y = 0

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

4 x^{2} - 16 x + 9 y^{2} + 54 y + 61 = 0

9 x^{2} + 16 y^{2} - 18 x + 64 y = 71

x^{2} + 4 y^{2} - 4 x - 8 y + 4 = 0

What is 9x^2+25y^2-18x-50y-191=0 ?
The solution to 9x^2+25y^2-18x-50y-191=0 is Ellipse with (h,k)=(1,1),a=5,b=3