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

x, x^{2} + 7 k + 3 k (x)^{2} = 0

16 x^{2} + 25 y^{2} + 64 x + 150 y - 111 = 0

\frac{( x - 1 ) ^{2}}{81} + \frac{( y - 2 ) ^{2}}{25} = 1

9 (x - 3)^{2} + 16 (y + 4)^{2} = 144

16 x^{2} + 4 y^{2} = 1

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