What is 5x^2+9y^2-80x+54y+221=0 ?

The solution to 5x^2+9y^2-80x+54y+221=0 is Ellipse with (h,k)=(8,-3),a=6,b=2sqrt(5)

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5x^2+9y^2-80x+54y+221=0

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

(h, k) = (8, - 3), a = 6, b = 25

Solution steps

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

Rewrite

5 x^{2} + 9 y^{2} - 80 x + 54 y + 221 = 0

in the form of the standard ellipse equation

\frac{( x - 8 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 3 ) ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (8, - 3), a = 6, b = 25

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (8, - 3), a = 6, b = 25

(\frac{x}{16})^{2} + \frac{y ^{2}}{81} = 1

11 x^{2} + 5 y^{2} + 110 x - 20 y + 240 = 0

\frac{x ^{2}}{cosh ^{2} ( β )} + \frac{y ^{2}}{sinh ^{2} ( β )} = 1

4 x^{2} = 36 - 9 y^{2}

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

What is 5x^2+9y^2-80x+54y+221=0 ?
The solution to 5x^2+9y^2-80x+54y+221=0 is Ellipse with (h,k)=(8,-3),a=6,b=2sqrt(5)