What is x^2+2y^2-8y-32=0 ?

The solution to x^2+2y^2-8y-32=0 is Ellipse with (h,k)=(0,2),a=2sqrt(10),b=2sqrt(5)

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x^2+2y^2-8y-32=0

x^{2} + 2 y^{2} - 8 y - 32 = 0

(h, k) = (0, 2), a = 210, b = 25

Solution steps

x^{2} + 2 y^{2} - 8 y - 32 = 0

Rewrite

x^{2} + 2 y^{2} - 8 y - 32 = 0

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 2 10 ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 2 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 2), a = 210, b = 25

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 210, b = 25

\frac{x ^{2}}{324} + \frac{y ^{2}}{400} = 1

3 x^{2} + 4 y^{2} - 12 x = 36

6 x^{2} + 8 y^{2} = 48

9 x^{2} + 25 y^{2} - 150 y = 0

x^{2} + 2 z^{2} = 1

What is x^2+2y^2-8y-32=0 ?
The solution to x^2+2y^2-8y-32=0 is Ellipse with (h,k)=(0,2),a=2sqrt(10),b=2sqrt(5)