What is 5x^2+10y^2=5 ?

The solution to 5x^2+10y^2=5 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(1/2)

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5x^2+10y^2=5

5 x^{2} + 10 y^{2} = 5

(h, k) = (0, 0), a = 1, b = \frac{1}{2}

Solution steps

5 x^{2} + 10 y^{2} = 5

Rewrite

5 x^{2} + 10 y^{2} = 5

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 1, b = \frac{1}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 1, b = \frac{1}{2}

3 x^{2} + 3 y^{2} + 36 y = 0

\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 7 ) ^{2}}{81} = 1

\frac{( x + 1 ) ^{2}}{100} + \frac{( y - 6 ) ^{2}}{64} = 1

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

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

What is 5x^2+10y^2=5 ?
The solution to 5x^2+10y^2=5 is Ellipse with (h,k)=(0,0),a=1,b=sqrt(1/2)