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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

2 x^{2} - 8 x + y^{2} - 6 y + 7 = 0

3 x^{2} + 2 y^{2} - 12 x + 6 y - 10 = 0

4.14 x^{2} + 3.92 y^{2} - 41.82 x - 82.62 y + 78 = 0

36 x^{2} + 8 y^{2} = 98

(\frac{y}{8})^{2} + (\frac{x}{7})^{2} = 1

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