What is 8x^2-96x+18y^2+144y+288=0 ?

The solution to 8x^2-96x+18y^2+144y+288=0 is Ellipse with (h,k)=(6,-4),a=6,b=4

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8x^2-96x+18y^2+144y+288=0

8 x^{2} - 96 x + 18 y^{2} + 144 y + 288 = 0

(h, k) = (6, - 4), a = 6, b = 4

Solution steps

8 x^{2} - 96 x + 18 y^{2} + 144 y + 288 = 0

Rewrite

8 x^{2} - 96 x + 18 y^{2} + 144 y + 288 = 0

in the form of the standard ellipse equation

\frac{( x - 6 ) ^{2}}{6 ^{2}} + \frac{( y - ( - 4 ) ) ^{2}}{4 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (6, - 4), a = 6, b = 4

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (6, - 4), a = 6, b = 4

2 x^{2} + 49 y^{2} = 98

4 x^{2} + 9 y^{2} - 40 x + 54 y + 1 + 5 = 0

9 x^{2} + 4 y^{2} - 18 x + 16 y - 119 = 0

25 x^{2} + 9 y^{2} - 100 x + 18 x - 116 = 0

\frac{( x - 4 ) ^{2}}{25} + \frac{( y + 6 ) ^{2}}{4} = 1

What is 8x^2-96x+18y^2+144y+288=0 ?
The solution to 8x^2-96x+18y^2+144y+288=0 is Ellipse with (h,k)=(6,-4),a=6,b=4