What is y^2=-0.25x^2+1 ?

The solution to y^2=-0.25x^2+1 is Ellipse with (h,k)=(0,0),a=2,b=1

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y^2=-0.25x^2+1

y^{2} = - 0.25 x^{2} + 1

(h, k) = (0, 0), a = 2, b = 1

Solution steps

y^{2} = - 0.25 x^{2} + 1

Rewrite

y^{2} = - 0.25 x^{2} + 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = 2, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = 2, b = 1

x, \frac{x ^{2}}{25} + \frac{Y ( x ) ^{2}}{4} = 1

\frac{( x - 4 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{25} = 1

\frac{( x + 6.5 ) ^{2}}{56.25} + \frac{( y - 3 ) ^{2}}{36} = 1

x^{2} - 4 x + 4 + y^{2} = \frac{x ^{2}}{4} - \frac{16 x}{4} + \frac{64}{4}

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

What is y^2=-0.25x^2+1 ?
The solution to y^2=-0.25x^2+1 is Ellipse with (h,k)=(0,0),a=2,b=1