What is 9x^2+25y^2-100y-125=0 ?

The solution to 9x^2+25y^2-100y-125=0 is Ellipse with (h,k)=(0,2),a=5,b=3

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9x^2+25y^2-100y-125=0

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

(h, k) = (0, 2), a = 5, b = 3

Solution steps

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

Rewrite

9 x^{2} + 25 y^{2} - 100 y - 125 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{5 ^{2}} + \frac{( y - 2 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 5, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 5, b = 3

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

16 x^{2} + 25 y^{2} - 96 x + 50 y - 231 = 0

(\frac{x ^{2}}{15}) + (\frac{y ^{2}}{16}) = 1

\frac{x ^{2}}{25} + \frac{z ^{2}}{64} = 1

\frac{x ^{2}}{4} + \frac{3 y ^{2}}{4} = 1

What is 9x^2+25y^2-100y-125=0 ?
The solution to 9x^2+25y^2-100y-125=0 is Ellipse with (h,k)=(0,2),a=5,b=3