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

The solution to 4x^2-2x+y^2-4=0 is Ellipse with (h,k)=(1/4 ,0),a=(sqrt(17))/4 ,b=(sqrt(17))/2

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

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

(h, k) = (\frac{1}{4}, 0), a = \frac{17}{4}, b = \frac{17}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{1}{4} ) ^{2}}{( \frac{17}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{17}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{4}, 0), a = \frac{17}{4}, b = \frac{17}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{4}, 0), b = \frac{17}{2}, a = \frac{17}{4}

\frac{x ^{2}}{49} + \frac{y ^{2}}{81} = 1

3 x^{2} + 5 y^{2} - 6 x + 2 y - 9 = 0

9 x^{2} + 25 y^{2} + 18 x - 100 y - 116 = 0

\frac{x ^{2}}{24} + \frac{y ^{2}}{9} = 1

9 x^{2} + 25 y^{2} - 36 x + 50 y - 164 = 0

What is 4x^2-2x+y^2-4=0 ?
The solution to 4x^2-2x+y^2-4=0 is Ellipse with (h,k)=(1/4 ,0),a=(sqrt(17))/4 ,b=(sqrt(17))/2