What is 9x^2+16y^2+96y-36x+36=0 ?

The solution to 9x^2+16y^2+96y-36x+36=0 is Ellipse with (h,k)=(2,-3),a=4,b=3

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

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

(h, k) = (2, - 3), a = 4, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 3), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (2, - 3), a = 4, b = 3

4 x^{2} + 8 x + 3 y^{2} + 6 y - 17 = 0

4 x^{2} + 16 y^{2} - 64 = 1

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

\frac{( x - 6 ) ^{2}}{36} + \frac{y ^{2}}{100} = 1

\frac{2 y}{x ^{2} + y ^{2}} < 1

What is 9x^2+16y^2+96y-36x+36=0 ?
The solution to 9x^2+16y^2+96y-36x+36=0 is Ellipse with (h,k)=(2,-3),a=4,b=3