What is 36x^2-36x+64y^2+256y+265=576 ?

The solution to 36x^2-36x+64y^2+256y+265=576 is Ellipse with (h,k)=(1/2 ,-2),a=4,b=3

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36x^2-36x+64y^2+256y+265=576

36 x^{2} - 36 x + 64 y^{2} + 256 y + 265 = 576

(h, k) = (\frac{1}{2}, - 2), a = 4, b = 3

Solution steps

36 x^{2} - 36 x + 64 y^{2} + 256 y + 265 = 576

Rewrite

36 x^{2} - 36 x + 64 y^{2} + 256 y + 265 = 576

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, - 2), a = 4, b = 3

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, - 2), a = 4, b = 3

x^{2} + y^{2} - 14 y = 0

\frac{x ^{2}}{( 2.67 ) ^{2}} + \frac{y ^{2}}{( 2.85 ) ^{2}} = 1

\frac{x ^{2}}{45} + \frac{y ^{2}}{9} = 1

\frac{( x - 2 ) ^{2}}{225} + \frac{( y - 8 ) ^{2}}{81} = 1

1 x^{2} + 3 y^{2} + 10 x + 9 y - 10 = 0

What is 36x^2-36x+64y^2+256y+265=576 ?
The solution to 36x^2-36x+64y^2+256y+265=576 is Ellipse with (h,k)=(1/2 ,-2),a=4,b=3