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

\frac{( x ^{2} - 4 x )}{4} + \frac{( y ^{2} - 6 y )}{9} = - 1

2 x^{2} + 4 y^{2} + 10 x + 8 y - 9 = 0

2 x^{2} + 5 y^{2} = 9

2 x^{2} + 5 y^{2} = 8

\frac{y ^{2}}{81} + \frac{( x + 5 ) ^{2}}{27} = 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