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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

25 x^{2} + 49 y^{2} = 49

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

\frac{( x - 4 ) ^{2}}{5} + \frac{( y - 6 ) ^{2}}{9} = 1

(\frac{( x + 2 ) ^{2}}{25}) + (\frac{( y - 1 ) ^{2}}{169}) = 1

5 y^{2} + 4 x^{2} = \frac{5}{4}

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