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

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

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0.25x^2+y^2=1

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

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

Solution steps

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

Rewrite

0.25 x^{2} + y^{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

5 (x - 3)^{2} = 20 - 4 (y - 6)^{2}

16 x^{2} + 36 y^{2} = 576

x^{2} + \frac{y ^{2}}{4} < 1

16 x^{2} + 25 y^{2} = 1

4 x^{2} + 2 y^{2} - 8 x + 12 y + 6 = 0

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