What is 5x^2+10y^2-80=0 ?

The solution to 5x^2+10y^2-80=0 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(2)

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5x^2+10y^2-80=0

5 x^{2} + 10 y^{2} - 80 = 0

(h, k) = (0, 0), a = 4, b = 22

Solution steps

5 x^{2} + 10 y^{2} - 80 = 0

Rewrite

5 x^{2} + 10 y^{2} - 80 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 4, b = 22

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 4, b = 22

9 y^{2} + 16 x^{2} - 90 y - 96 x + 225 = 0

3 x^{2} + 2 y^{2} - 12 = 0

\frac{y ^{2}}{16} + \frac{x ^{2}}{25} = 1

22 x^{2} + 2 y^{2} - 4 x + 12 y - 12 = 0

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

What is 5x^2+10y^2-80=0 ?
The solution to 5x^2+10y^2-80=0 is Ellipse with (h,k)=(0,0),a=4,b=2sqrt(2)