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

2 x^{2} + 4 y^{2} + 9 x + 9 y - 13 = 0

x^{2} + y^{2} + (x - 1)^{2} = 1

\frac{x ^{2}}{8 ^{2}} + \frac{y ^{2}}{7 ^{2}} = 1

\frac{x ^{2}}{25} + \frac{y ^{2}}{6 ^{2}} = 1

\frac{( X + 3 ) ^{2}}{49} + \frac{( Y + 2 ) ^{2}}{36} = 1

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