What is 1-x^2-y^2=5 ?

The solution to 1-x^2-y^2=5 is Ellipse with (h,k)=(0,0),a=2,b=2

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1-x^2-y^2=5

1 - x^{2} - y^{2} = 5

(h, k) = (0, 0), a = 2, b = 2

Solution steps

1 - x^{2} - y^{2} = 5

Rewrite

1 - x^{2} - y^{2} = 5

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 2

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 2, a = 2

36 (x - \frac{1}{2})^{2} - \frac{1}{4} + 64 (y + 2)^{2} - 4 + 265 = 576

\frac{x ^{2}}{4 ^{2}} + \frac{y ^{2}}{6 ^{2}} = 1

7 x^{2} + y^{2} = 8

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

4 x^{2} + 32 x + 9 y^{2} - 18 y + 37 = 0

What is 1-x^2-y^2=5 ?
The solution to 1-x^2-y^2=5 is Ellipse with (h,k)=(0,0),a=2,b=2