What is ((x-3)^2)/2+(y+5)^2=8 ?

The solution to ((x-3)^2)/2+(y+5)^2=8 is Ellipse with (h,k)=(3,-5),a=4,b=2sqrt(2)

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((x-3)^2)/2+(y+5)^2=8

\frac{( x - 3 ) ^{2}}{2} + (y + 5)^{2} = 8

(h, k) = (3, - 5), a = 4, b = 22

Solution steps

\frac{( x - 3 ) ^{2}}{2} + (y + 5)^{2} = 8

Rewrite

\frac{( x - 3 ) ^{2}}{2} + (y + 5)^{2} = 8

in the form of the standard ellipse equation

\frac{( x - 3 ) ^{2}}{4 ^{2}} + \frac{( y - ( - 5 ) ) ^{2}}{( 2 2 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (3, - 5), a = 4, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (3, - 5), a = 4, b = 22

(\frac{x - 2}{9})^{2} + (\frac{y + 2}{25})^{2} = 1

25 x^{2} + 64 y^{2} - 400 x - 640 y + 1600 = 0

9 x^{2} + 25 y^{2} = 64

y^{2} = - 6 x^{2} + 4

x^{2} + 2 y^{2} + 2 x - 20 y = - 43

What is ((x-3)^2)/2+(y+5)^2=8 ?
The solution to ((x-3)^2)/2+(y+5)^2=8 is Ellipse with (h,k)=(3,-5),a=4,b=2sqrt(2)