What is 9= 1/(x^2+y^2-7) ?

The solution to 9= 1/(x^2+y^2-7) is Ellipse with (h,k)=(0,0),a= 8/3 ,b= 8/3

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9= 1/(x^2+y^2-7)

9 = \frac{1}{x ^{2} + y ^{2} - 7}

(h, k) = (0, 0), a = \frac{8}{3}, b = \frac{8}{3}

Solution steps

9 = \frac{1}{x ^{2} + y ^{2} - 7}

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{8}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{8}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{8}{3}, b = \frac{8}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{8}{3}, a = \frac{8}{3}

What is 9= 1/(x^2+y^2-7) ?
The solution to 9= 1/(x^2+y^2-7) is Ellipse with (h,k)=(0,0),a= 8/3 ,b= 8/3