What is 8x^2+9y^2-16x-18y-55=0 ?

The solution to 8x^2+9y^2-16x-18y-55=0 is Ellipse with (h,k)=(1,1),a=3,b=2sqrt(2)

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8x^2+9y^2-16x-18y-55=0

8 x^{2} + 9 y^{2} - 16 x - 18 y - 55 = 0

(h, k) = (1, 1), a = 3, b = 22

Solution steps

8 x^{2} + 9 y^{2} - 16 x - 18 y - 55 = 0

Rewrite

8 x^{2} + 9 y^{2} - 16 x - 18 y - 55 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, 1), a = 3, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, 1), a = 3, b = 22

\frac{x ^{2}}{576} + \frac{y ^{2}}{676} = 1

9 x^{2} + y^{2} - 18 x - 6 y + 9 = 0

25 x^{2} + 10 y^{2} = 50

\frac{( x + 5 ) ^{2}}{100} + \frac{( y - 4 ) ^{2}}{64} = 1

2 x^{2} + 7 y^{2} = 14

What is 8x^2+9y^2-16x-18y-55=0 ?
The solution to 8x^2+9y^2-16x-18y-55=0 is Ellipse with (h,k)=(1,1),a=3,b=2sqrt(2)