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

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

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10y^2+x^2=5

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

(h, k) = (0, 0), a = 5, b = \frac{1}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 5, 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 = 5, b = \frac{1}{2}

9 x^{2} + 4 (y - 2)^{2} = 36

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

1 x^{2} + 4 y^{2} + 10 x + 8 y - 19 = 0

36 x^{2} + 9 y^{2} + 288 x - 90 y + 477 = 0

(\frac{x ^{2}}{72}) + (\frac{y ^{2}}{21}) = 1

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