What is 9x^2+16y^2+36x-160y+292=0 ?

The solution to 9x^2+16y^2+36x-160y+292=0 is Ellipse with (h,k)=(-2,5),a=4,b=3

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9x^2+16y^2+36x-160y+292=0

9 x^{2} + 16 y^{2} + 36 x - 160 y + 292 = 0

(h, k) = (- 2, 5), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} + 36 x - 160 y + 292 = 0

Rewrite

9 x^{2} + 16 y^{2} + 36 x - 160 y + 292 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 5), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 5), a = 4, b = 3

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

\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

What is 9x^2+16y^2+36x-160y+292=0 ?
The solution to 9x^2+16y^2+36x-160y+292=0 is Ellipse with (h,k)=(-2,5),a=4,b=3