What is 9x^2-54x+25y^2-200y=-256 ?

The solution to 9x^2-54x+25y^2-200y=-256 is Ellipse with (h,k)=(3,4),a=5,b=3

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9x^2-54x+25y^2-200y=-256

9 x^{2} - 54 x + 25 y^{2} - 200 y = - 256

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

Solution steps

9 x^{2} - 54 x + 25 y^{2} - 200 y = - 256

Rewrite

9 x^{2} - 54 x + 25 y^{2} - 200 y = - 256

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

y^{2} = 2 x

y = x^{2} - 24 x - 12

\frac{x ^{2}}{16} - \frac{y ^{2}}{9} = 1

x^{2} - 12 x + 16 y + 68 = 0

10 x^{2} + 4 y^{2} + 2 x + 16 y = 144

What is 9x^2-54x+25y^2-200y=-256 ?
The solution to 9x^2-54x+25y^2-200y=-256 is Ellipse with (h,k)=(3,4),a=5,b=3