What is 25x^2+9y^2+100x+36y-89=0 ?

The solution to 25x^2+9y^2+100x+36y-89=0 is Ellipse with (h,k)=(-2,-2),a=3,b=5

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25x^2+9y^2+100x+36y-89=0

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

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

Solution steps

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

Rewrite

25 x^{2} + 9 y^{2} + 100 x + 36 y - 89 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

\frac{( x - 12 ) ^{2}}{100} + \frac{( y + 7 ) ^{2}}{36} = 1

12 x^{2} + 10 y^{2} = 120

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

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

What is 25x^2+9y^2+100x+36y-89=0 ?
The solution to 25x^2+9y^2+100x+36y-89=0 is Ellipse with (h,k)=(-2,-2),a=3,b=5