What is 4x^2+9y^2+16x-54y+61=0 ?

The solution to 4x^2+9y^2+16x-54y+61=0 is Ellipse with (h,k)=(-2,3),a=3,b=2

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4x^2+9y^2+16x-54y+61=0

4 x^{2} + 9 y^{2} + 16 x - 54 y + 61 = 0

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

Solution steps

4 x^{2} + 9 y^{2} + 16 x - 54 y + 61 = 0

Rewrite

4 x^{2} + 9 y^{2} + 16 x - 54 y + 61 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

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

\frac{x ^{2}}{\frac{81}{4}} + \frac{y ^{2}}{\frac{25}{16}} = 1

9 x^{2} + 16 y^{2} + 72 x + 128 y + 256 = 0

9 x^{2} + 4 y^{2} - 18 x - 16 y - 11 = 0

x^{2} + 4 y^{2} - 25 = 0

What is 4x^2+9y^2+16x-54y+61=0 ?
The solution to 4x^2+9y^2+16x-54y+61=0 is Ellipse with (h,k)=(-2,3),a=3,b=2