What is 25x^2+9y^2+50x-54y-119=0 ?

The solution to 25x^2+9y^2+50x-54y-119=0 is Ellipse with (h,k)=(-1,3),a=3,b=5

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25x^2+9y^2+50x-54y-119=0

25 x^{2} + 9 y^{2} + 50 x - 54 y - 119 = 0

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

Solution steps

25 x^{2} + 9 y^{2} + 50 x - 54 y - 119 = 0

Rewrite

25 x^{2} + 9 y^{2} + 50 x - 54 y - 119 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

\frac{( x - 0.5 ) ^{2}}{10} + \frac{( y - 3 ) ^{2}}{5} = 1

\frac{x ^{2}}{9} + \frac{y ^{2}}{40} = 1

x^{2} + 2 y^{2} < 1

(3 x - 3)^{2} + (2 y - 4)^{2} = 43 + 9 + 16

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

What is 25x^2+9y^2+50x-54y-119=0 ?
The solution to 25x^2+9y^2+50x-54y-119=0 is Ellipse with (h,k)=(-1,3),a=3,b=5