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

\frac{( x - 2 ) ^{2}}{5} + \frac{( y + 1 ) ^{2}}{4} = 1

6 x^{2} + y^{2} + 12 x = 0

2 - \frac{2 - 2 x}{2 x - x ^{2} - y ^{2}} = 0

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

X^{2} + 2 \cdot Y^{2} - 2 \cdot X - 4 \cdot Y - 8 = 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