What is 9x^2+16y^2-160y+256=0 ?

The solution to 9x^2+16y^2-160y+256=0 is Ellipse with (h,k)=(0,5),a=4,b=3

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9x^2+16y^2-160y+256=0

9 x^{2} + 16 y^{2} - 160 y + 256 = 0

(h, k) = (0, 5), a = 4, b = 3

Solution steps

9 x^{2} + 16 y^{2} - 160 y + 256 = 0

Rewrite

9 x^{2} + 16 y^{2} - 160 y + 256 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{4 ^{2}} + \frac{( y - 5 ) ^{2}}{3 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 5), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 5), a = 4, b = 3

\frac{x ^{2}}{10} + \frac{y ^{2}}{2} = 1

4 x^{2} + 25 y^{2} - 200 y + 300 = 0

\frac{X ^{2}}{16} + (y - 4)^{2} = 1

\frac{x ^{2}}{2 0 ^{2}} + \frac{y ^{2}}{1 5 ^{2}} = 1

25 x^{2} + 16 y^{2} - 100 x - 300 = 0

What is 9x^2+16y^2-160y+256=0 ?
The solution to 9x^2+16y^2-160y+256=0 is Ellipse with (h,k)=(0,5),a=4,b=3