What is y^2=x(4-x)2 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^2=x(4-x)2

y^{2} = x (4 - x) 2

(h, k) = (2, 0), a = 2, b = 22

Solution steps

y^{2} = x (4 - x) \cdot 2

Rewrite

y^{2} - x (4 - x) 2 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, 0), a = 2, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, 0), b = 22, a = 2

25 x^{2} + 16 y^{2} + 50 x - 96 y - 231 = 0

4 x^{2} + y^{2} - 24 x + 4 y + 24 = 0

\frac{x - 3 y}{x ^{2} + y ^{2}} + 1 = 0

a^{2} + \frac{a ^{2}}{2} + \frac{b ^{2}}{2} = 26

x^{2} + y^{2} = - 12 y

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