What is 8x^2-176x+9y^2-18y+905=0 ?

The solution to 8x^2-176x+9y^2-18y+905=0 is Ellipse with (h,k)=(11,1),a=3,b=2sqrt(2)

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8x^2-176x+9y^2-18y+905=0

8 x^{2} - 176 x + 9 y^{2} - 18 y + 905 = 0

(h, k) = (11, 1), a = 3, b = 22

Solution steps

8 x^{2} - 176 x + 9 y^{2} - 18 y + 905 = 0

Rewrite

8 x^{2} - 176 x + 9 y^{2} - 18 y + 905 = 0

in the form of the standard ellipse equation

\frac{( x - 11 ) ^{2}}{3 ^{2}} + \frac{( y - 1 ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (11, 1), a = 3, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (11, 1), a = 3, b = 22

9 x^{2} + 25 y^{2} = 400

36 - 4 x^{2} - 9 y^{2} = 0

\frac{12 ( x - 1 ) ^{2}}{24} + \frac{3 y ^{2}}{24} = \frac{24}{24}

10 x^{2} - 70 = - 7 y^{2}

2 x^{2} + 3 (y - 2)^{2} = 20

What is 8x^2-176x+9y^2-18y+905=0 ?
The solution to 8x^2-176x+9y^2-18y+905=0 is Ellipse with (h,k)=(11,1),a=3,b=2sqrt(2)