What is (x^2)/8+(y^2)/(12)=1 ?

The solution to (x^2)/8+(y^2)/(12)=1 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=2sqrt(3)

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(x^2)/8+(y^2)/(12)=1

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

(h, k) = (0, 0), a = 22, b = 23

Solution steps

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

Rewrite

\frac{x ^{2}}{8} + \frac{y ^{2}}{12} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 22, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 23, a = 22

7 x^{2} + 2 y^{2} - 14 = 0

\frac{( x - 3 ) ^{2}}{16} + \frac{( y + 1 ) ^{2}}{4} = 1

9 x^{2} + 49 y^{2} + 108 x - 196 y + 79 = 0

- 2 y^{2} - x^{2} + y + 79 = 0

41 x^{2} + 16 y^{2} + 246 x - 192 y + 289 = 0

What is (x^2)/8+(y^2)/(12)=1 ?
The solution to (x^2)/8+(y^2)/(12)=1 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=2sqrt(3)