What is 9x^2+18x+16y^2-96y+9=0 ?

The solution to 9x^2+18x+16y^2-96y+9=0 is Ellipse with (h,k)=(-1,3),a=4,b=3

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9x^2+18x+16y^2-96y+9=0

9 x^{2} + 18 x + 16 y^{2} - 96 y + 9 = 0

(h, k) = (- 1, 3), a = 4, b = 3

Solution steps

9 x^{2} + 18 x + 16 y^{2} - 96 y + 9 = 0

Rewrite

9 x^{2} + 18 x + 16 y^{2} - 96 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 3), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 3), a = 4, b = 3

3 x^{2} + 2 y^{2} \leq 13950

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{9} = 1

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

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

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

What is 9x^2+18x+16y^2-96y+9=0 ?
The solution to 9x^2+18x+16y^2-96y+9=0 is Ellipse with (h,k)=(-1,3),a=4,b=3