What is 5x^2+9y^2-20x+54y+56=0 ?

The solution to 5x^2+9y^2-20x+54y+56=0 is Ellipse with (h,k)=(2,-3),a=3,b=sqrt(5)

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5x^2+9y^2-20x+54y+56=0

5 x^{2} + 9 y^{2} - 20 x + 54 y + 56 = 0

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

Solution steps

5 x^{2} + 9 y^{2} - 20 x + 54 y + 56 = 0

Rewrite

5 x^{2} + 9 y^{2} - 20 x + 54 y + 56 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

x^{2} + 4 y^{2} = 8

x^{2} + 9 y^{2} - 9 = 0

4 x^{2} + 9 y^{2} - 225 = 0

16 x^{2} + 25 y^{2} - 128 x + 150 y + 81 = 0

4 x^{2} + y^{2} = 9

What is 5x^2+9y^2-20x+54y+56=0 ?
The solution to 5x^2+9y^2-20x+54y+56=0 is Ellipse with (h,k)=(2,-3),a=3,b=sqrt(5)