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

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

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

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

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

Solution steps

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

Rewrite

2 - 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}

9 x^{2} + 16 y^{2} + 54 x - 32 y - 47 = 0

16 x^{2} + 25 y^{2} - 32 x - 150 y - 159 = 0

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

\frac{( x - 2 ) ^{2}}{9} + \frac{( y - 1 ) ^{2}}{4} = 1

x^{2} + y^{2} = 9 y

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