What is (100)/(1+x^2+2y^2)=1 ?

The solution to (100)/(1+x^2+2y^2)=1 is Ellipse with (h,k)=(0,0),a=3sqrt(11),b=(3sqrt(11))/(sqrt(2))

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(100)/(1+x^2+2y^2)=1

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 1

(h, k) = (0, 0), a = 311, b = \frac{3 11}{2}

Solution steps

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 1

Rewrite

\frac{100}{1 + x ^{2} + 2 y ^{2}} = 1

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( 3 11 ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{3 11}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 311, b = \frac{3 11}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 311, b = \frac{3 11}{2}

81 x^{2} + 49 y^{2} + 486 x - 490 y - 2015 = 0

0 = 1 + 2 x^{2} + 2 y^{2}

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

16 x^{2} + 9 y^{2} - 32 x + 54 y - 47 = 0

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

What is (100)/(1+x^2+2y^2)=1 ?
The solution to (100)/(1+x^2+2y^2)=1 is Ellipse with (h,k)=(0,0),a=3sqrt(11),b=(3sqrt(11))/(sqrt(2))