What is ((x-5)^2)/8+((y+1)^2)/(12)=1 ?

The solution to ((x-5)^2)/8+((y+1)^2)/(12)=1 is Ellipse with (h,k)=(5,-1),a=2sqrt(2),b=2sqrt(3)

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((x-5)^2)/8+((y+1)^2)/(12)=1

\frac{( x - 5 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{12} = 1

(h, k) = (5, - 1), a = 22, b = 23

Solution steps

\frac{( x - 5 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{12} = 1

Rewrite

\frac{( x - 5 ) ^{2}}{8} + \frac{( y + 1 ) ^{2}}{12} = 1

in the form of the standard ellipse equation

\frac{( x - 5 ) ^{2}}{( 2 2 ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (5, - 1), a = 22, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (5, - 1), b = 23, a = 22

\frac{x ^{2}}{49} + \frac{y ^{2}}{48} = 1

3 x^{2} + 3 y^{2} + 24 y = 0

5 x^{2} + 7 y^{2} = 9

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

\frac{( x + 2 ) ^{2}}{9} + \frac{( y - 7 ) ^{2}}{64} = 1

What is ((x-5)^2)/8+((y+1)^2)/(12)=1 ?
The solution to ((x-5)^2)/8+((y+1)^2)/(12)=1 is Ellipse with (h,k)=(5,-1),a=2sqrt(2),b=2sqrt(3)