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

The solution to x^2+8y^2=32 is Ellipse with (h,k)=(0,0),a=4sqrt(2),b=2

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x^2+8y^2=32

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

(h, k) = (0, 0), a = 42, b = 2

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 4 2 ) ^{2}} + \frac{( y - 0 ) ^{2}}{2 ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 42, b = 2

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 42, b = 2

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

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{16} = 1

4 = 36 - 9 x^{2} - 4 y^{2}

9 x^{2} + 25 y^{2} - 18 x - 100 y - 116 = 0

What is x^2+8y^2=32 ?
The solution to x^2+8y^2=32 is Ellipse with (h,k)=(0,0),a=4sqrt(2),b=2