What is 0.5=4x^2+y^2 ?

The solution to 0.5=4x^2+y^2 is Ellipse with (h,k)=(0,0),a=0.35355…,b=0.70710…

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0.5=4x^2+y^2

0.5 = 4 x^{2} + y^{2}

(h, k) = (0, 0), a = 0.35355 \dots, b = 0.70710 \dots

Solution steps

0.5 = 4 x^{2} + y^{2}

Rewrite

0.5 = 4 x^{2} + y^{2}

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{0.35355 \dots ^{2}} + \frac{( y - 0 ) ^{2}}{0.70710 \dots ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = 0.35355 \dots, b = 0.70710 \dots

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 0.70710 \dots, a = 0.35355 \dots

\frac{x ^{2}}{9} + y^{2} > 9

\frac{( x + 8 ) ^{2}}{20} + \frac{( y + 36 ) ^{2}}{36} = 1

4 x^{2} + y^{2} - 16 x - 2 y + 1 = 0

5 x^{2} + z^{2} = 100

\frac{( x + 2 ) ^{2}}{16} + \frac{( y + 3 ) ^{2}}{36} = 1

What is 0.5=4x^2+y^2 ?
The solution to 0.5=4x^2+y^2 is Ellipse with (h,k)=(0,0),a=0.35355…,b=0.70710…