What is 1-x^2-5y^2>0 ?

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

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1-x^2-5y^2>0

1 - x^{2} - 5 y^{2} > 0

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

Solution steps

1 - x^{2} - 5 y^{2} > 0

Rewrite

1 - x^{2} - 5 y^{2} > 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

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}{5}

\frac{( x - 3 ) ^{2}}{25} + \frac{( y - 5 ) ^{2}}{16} = 1

13 x^{2} + 4 y^{2} - 52 x - 24 y + 36 = 0

36 - 9 x^{2} - 4 y^{2} \geq 0

(x 3)^{2} + (y + 2)^{2} = 25

(\frac{( y - 8 )}{40})^{2} + (\frac{( x + 10 )}{211})^{2} = 1

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