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

The solution to (100)/(1+x^2+2y^2)=2 is Ellipse with (h,k)=(0,0),a=7,b= 7/(sqrt(2))

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

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

(h, k) = (0, 0), a = 7, b = \frac{7}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{7 ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 7, b = \frac{7}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 7, b = \frac{7}{2}

\frac{( x + 0 ) ^{2}}{\frac{225}{25}} + \frac{( y - 1 ) ^{2}}{\frac{225}{9}} = 1

3 = x^{2} + 9 y^{2}

\frac{( x - 1 ) ^{2}}{16} + \frac{y ^{2}}{9} = 1

\frac{( x - 1 ) ^{2}}{4} + \frac{( y + 1 ) ^{2}}{9} = 1

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

What is (100)/(1+x^2+2y^2)=2 ?
The solution to (100)/(1+x^2+2y^2)=2 is Ellipse with (h,k)=(0,0),a=7,b= 7/(sqrt(2))