What is 9y^2+16x^2-90y-96x+225=0 ?

The solution to 9y^2+16x^2-90y-96x+225=0 is Ellipse with (h,k)=(3,5),a=3,b=4

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9y^2+16x^2-90y-96x+225=0

9 y^{2} + 16 x^{2} - 90 y - 96 x + 225 = 0

(h, k) = (3, 5), a = 3, b = 4

Solution steps

9 y^{2} + 16 x^{2} - 90 y - 96 x + 225 = 0

Rewrite

9 y^{2} + 16 x^{2} - 90 y - 96 x + 225 = 0

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{3 ^{2}} + \frac{( y - 5 ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, 5), a = 3, b = 4

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (3, 5), b = 4, a = 3

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

\frac{y ^{2}}{16} + \frac{x ^{2}}{25} = 1

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

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

3 x^{2} + 4 y^{2} - 5 x + 2 y + 1 = 0

What is 9y^2+16x^2-90y-96x+225=0 ?
The solution to 9y^2+16x^2-90y-96x+225=0 is Ellipse with (h,k)=(3,5),a=3,b=4