-x^2-4=y^2

Solution

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

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

Solution steps

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

Rewrite

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

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

x^{2} + 10 y^{2} - 6 x + 20 y + 18 = 0

\frac{( x - 1 ) ^{2}}{7 ^{2}} + \frac{( y - 1 ) ^{2}}{3 ^{2}} = 1

\frac{( x - 1 ) ^{2}}{36} + \frac{( y + 2 ) ^{2}}{25} = 1

4 x^{2} + y^{2} - 8 x + 4 y - 4 = 0

x^{2} + 4 y^{2} - 6 x - 16 y + 21 > 0

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