What is 25x^2+9y^2-18y-216=0 ?

The solution to 25x^2+9y^2-18y-216=0 is Ellipse with (h,k)=(0,1),a=3,b=5

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25x^2+9y^2-18y-216=0

25 x^{2} + 9 y^{2} - 18 y - 216 = 0

(h, k) = (0, 1), a = 3, b = 5

Solution steps

25 x^{2} + 9 y^{2} - 18 y - 216 = 0

Rewrite

25 x^{2} + 9 y^{2} - 18 y - 216 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 1), a = 3, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 1), b = 5, a = 3

\frac{x ^{2}}{63500} + \frac{y ^{2}}{50900} = 1

4 x^{2} + 9 y^{2} + 24 x - 36 y + 36 = 0

9 x^{2} + 16 y^{2} - 36 x + 96 y + 36 = 0

x^{2} - 4 x + 3 y^{2} + y = 12

2 x^{2} + 8 y^{2} - 12 = 0

What is 25x^2+9y^2-18y-216=0 ?
The solution to 25x^2+9y^2-18y-216=0 is Ellipse with (h,k)=(0,1),a=3,b=5