What is 4= 1/(x^2+y^2-7) ?

The solution to 4= 1/(x^2+y^2-7) is Ellipse with (h,k)=(0,0),a=(sqrt(29))/2 ,b=(sqrt(29))/2

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4= 1/(x^2+y^2-7)

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

(h, k) = (0, 0), a = \frac{29}{2}, b = \frac{29}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{29}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{29}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{29}{2}, b = \frac{29}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = \frac{29}{2}, a = \frac{29}{2}

6.25 x^{2} + 16 y^{2} - 1.25 x + 64 y - 29.75 = 0

\frac{( x - 1 ) ^{2}}{4} + \frac{( y - 5 ) ^{2}}{25} = 1

\frac{x ^{2}}{36} + \frac{y ^{2}}{5.9 1 ^{2}} = 1

16 x^{2} + 25 y^{2} - 128 x + 100 y = 0

\frac{( ( x + 0 ) ^{2} )}{40} + \frac{( ( y + 0 ) ^{2} )}{32} = 1

What is 4= 1/(x^2+y^2-7) ?
The solution to 4= 1/(x^2+y^2-7) is Ellipse with (h,k)=(0,0),a=(sqrt(29))/2 ,b=(sqrt(29))/2