What is 2a^2+b^2=a+b ?

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

Popular >

2a^2+b^2=a+b

2 a^{2} + b^{2} = a + b

(h, k) = (\frac{1}{4}, \frac{1}{2}), a = \frac{3}{4}, b = \frac{3}{2 2}

Solution steps

2 a^{2} + b^{2} = a + b

Rewrite

2 a^{2} + b^{2} = a + b

in the form of the standard ellipse equation

\frac{( a - \frac{1}{4} ) ^{2}}{( \frac{3}{4} ) ^{2}} + \frac{( b - \frac{1}{2} ) ^{2}}{( \frac{3}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (\frac{1}{4}, \frac{1}{2}), a = \frac{3}{4}, b = \frac{3}{2 2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (\frac{1}{4}, \frac{1}{2}), b = \frac{3}{2 2}, a = \frac{3}{4}

\frac{( x - 1 ) ^{2}}{16} + \frac{( y - 4 ) ^{2}}{52} = 1

x^{2} + 3 (y^{2}) = 84

\frac{2}{4} (3 x^{2} + y^{2}) - 2 (x - y) = 0

16 x^{2} + y^{2} - 64 x + 8 y + 16 = 0

\frac{1}{2} x^{2} + 6 y^{2} - 5 x + \frac{1}{4} y + 8 = 0

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