What is 4x^2+2y^2-4x+2y+1=0 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^2+2y^2-4x+2y+1=0

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

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

(x + 5)^{2} + \frac{3}{10} y^{2} = 34

4 - 2 x^{2} - 3 y^{2} = 0

x^{2} + 4 y^{2} - x + 2 y = 8

6 x^{2} + 7 y^{2} = 6

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