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

The solution to x^2+1/4 y^2=x+y is Ellipse with (h,k)=(1/2 ,2),a=(sqrt(5))/2 ,b=sqrt(5)

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

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

(h, k) = (\frac{1}{2}, 2), a = \frac{5}{2}, b = 5

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - \frac{1}{2} ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - 2 ) ^{2}}{( 5 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{2}, 2), a = \frac{5}{2}, b = 5

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{2}, 2), b = 5, a = \frac{5}{2}

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

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

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

\frac{( x + 3 ) ^{2}}{6 ^{2}} + \frac{( y + 7 ) ^{2}}{2 ^{2}} = 1

25 x^{(2)} - 200 x + y^{(2)} + 4 y + 379 = 0

What is x^2+1/4 y^2=x+y ?
The solution to x^2+1/4 y^2=x+y is Ellipse with (h,k)=(1/2 ,2),a=(sqrt(5))/2 ,b=sqrt(5)