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

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

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

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

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

Solution steps

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

Rewrite

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

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

\frac{x ^{2}}{9} + \frac{x ^{2}}{16} + \frac{z ^{2}}{9} = 1

9 x^{2} + 4 y^{2} - 72 x - 16 y + 124 = 0

8 x^{2} + 9 y^{2} + 24 x + 18 y = 10

x^{2} + y^{2} + 5 y = 0

1 x^{2} + 4 y^{2} + 10 x + 9 y - 10 = 0

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