What is 25x^2+9y^2+100x-54y-44=0 ?

The solution to 25x^2+9y^2+100x-54y-44=0 is Ellipse with (h,k)=(-2,3),a=3,b=5

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25x^2+9y^2+100x-54y-44=0

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

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

Solution steps

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

Rewrite

25 x^{2} + 9 y^{2} + 100 x - 54 y - 44 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

2 x^{2} + 4 y^{2} = 8

9 z^{2} + y^{2} = 36

\frac{( x - 3 ) ^{2}}{12} + \frac{y ^{2}}{16} = 1

4 a^{2} + 9 b^{2} = 25

What is 25x^2+9y^2+100x-54y-44=0 ?
The solution to 25x^2+9y^2+100x-54y-44=0 is Ellipse with (h,k)=(-2,3),a=3,b=5