What is the axis 6x^2+8y^2+12x-32y=178 ?

The axis 6x^2+8y^2+12x-32y=178 is semi-major axis a=6, semi-minor axis b=3sqrt(3)

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axis 6x^2+8y^2+12x-32y=178

axis

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178

semi - major axis a = 6, semi - minor axis b = 33

Solution steps

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178

Rewrite

6 x^{2} + 8 y^{2} + 12 x - 32 y = 178

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 2), a = 6, b = 33

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 1, 2), a = 6, b = 33

3 x^{2} + 12 x + 4 y^{2} - 40 y + 100 = 0

\frac{( x - 3 ) ^{2}}{49} + \frac{( y + 6 ) ^{2}}{100} = 1

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

5 x^{2} + 2 y^{2} = 10

x^{2} + 4 y^{2} - 6 x + 8 y + 9 = 0

What is the axis 6x^2+8y^2+12x-32y=178 ?
The axis 6x^2+8y^2+12x-32y=178 is semi-major axis a=6, semi-minor axis b=3sqrt(3)