What is (4/(sqrt(9-x^2-y^2)))^2=16 ?

The solution to (4/(sqrt(9-x^2-y^2)))^2=16 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=2sqrt(2)

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(4/(sqrt(9-x^2-y^2)))^2=16

(\frac{4}{9 - x ^{2} - y ^{2}})^{2} = 16

(h, k) = (0, 0), a = 22, b = 22

Solution steps

(\frac{4}{9 - x ^{2} - y ^{2}})^{2} = 16

Rewrite

(\frac{4}{9 - x ^{2} - y ^{2}})^{2} = 16

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 22, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 22, a = 22

\frac{( y - 8 ) ^{2}}{9} + \frac{( x - 5 ) ^{2}}{4} = 1

0 = 4 x^{2} + y^{2} + 1

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

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

11 x^{2} + 13 y^{2} - 143 = 0

What is (4/(sqrt(9-x^2-y^2)))^2=16 ?
The solution to (4/(sqrt(9-x^2-y^2)))^2=16 is Ellipse with (h,k)=(0,0),a=2sqrt(2),b=2sqrt(2)