What is 25x^2+9y^2-100x+18y-116=0 ?

The solution to 25x^2+9y^2-100x+18y-116=0 is Ellipse with (h,k)=(2,-1),a=3,b=5

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25x^2+9y^2-100x+18y-116=0

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

(h, k) = (2, - 1), a = 3, b = 5

Solution steps

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

Rewrite

25 x^{2} + 9 y^{2} - 100 x + 18 y - 116 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 1), b = 5, a = 3

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

y^{2} = - 36 x

x^{2} + 4 y^{2} = 36

y, x^{2} - 6 x + 9 - 4 y^{2} = 0

y^{2} + x^{2} = 25

What is 25x^2+9y^2-100x+18y-116=0 ?
The solution to 25x^2+9y^2-100x+18y-116=0 is Ellipse with (h,k)=(2,-1),a=3,b=5