What is 0=4x^2+y^2+1 ?

The solution to 0=4x^2+y^2+1 is Ellipse with (h,k)=(0,0),a= 1/2 ,b=1

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0=4x^2+y^2+1

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

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = 1

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 1, a = \frac{1}{2}

\frac{x ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{( a - 16 )} = 1

11 x^{2} + 13 y^{2} - 143 = 0

x^{2} + 3 y^{2} - 12 y + 9 = 0

4 x^{2} + 9 y^{2} - 40 x + 36 y + 100 = 0

What is 0=4x^2+y^2+1 ?
The solution to 0=4x^2+y^2+1 is Ellipse with (h,k)=(0,0),a= 1/2 ,b=1