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

The solution to 4=4x^2+y^2+1 is Ellipse with (h,k)=(0,0),a=(sqrt(3))/2 ,b=sqrt(3)

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

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

(h, k) = (0, 0), a = \frac{3}{2}, b = 3

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - 0 ) ^{2}}{( \frac{3}{2} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{3}{2}, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, 0), b = 3, a = \frac{3}{2}

What is 4=4x^2+y^2+1 ?
The solution to 4=4x^2+y^2+1 is Ellipse with (h,k)=(0,0),a=(sqrt(3))/2 ,b=sqrt(3)