What is 25x^2+36y^2+100x+72y-764=0 ?

The solution to 25x^2+36y^2+100x+72y-764=0 is Ellipse with (h,k)=(-2,-1),a=6,b=5

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25x^2+36y^2+100x+72y-764=0

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

(h, k) = (- 2, - 1), a = 6, b = 5

Solution steps

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

Rewrite

25 x^{2} + 36 y^{2} + 100 x + 72 y - 764 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{6 ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{5 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - 1), a = 6, b = 5

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - 1), a = 6, b = 5

\frac{2 x ^{2}}{25} + \frac{( y - 3 ) ^{2}}{49} = 1

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

12 x^{2} + 4 y^{2} - 24 x - 4 y + 1 = 0

\frac{( x - 2 ) ^{2}}{25} + \frac{( y + 1 ) ^{2}}{9} = 1

4 x^{2} + 5 y^{2} = 20

What is 25x^2+36y^2+100x+72y-764=0 ?
The solution to 25x^2+36y^2+100x+72y-764=0 is Ellipse with (h,k)=(-2,-1),a=6,b=5