What is 4x^{(2)}+9y^{(2)}=2 ?

The solution to 4x^{(2)}+9y^{(2)}=2 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=(sqrt(2))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

4x^{(2)}+9y^{(2)}=2

4 x^{(2)} + 9 y^{(2)} = 2

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{2}{3}

Solution steps

4 x^{2} + 9 y^{2} = 2

Rewrite

4 x^{2} + 9 y^{2} = 2

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 0), a = \frac{1}{2}, b = \frac{2}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 0), a = \frac{1}{2}, b = \frac{2}{3}

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

3 y^{2} + 3 x^{2} - 12 y = 0

25 x^{2} + 4 y^{2} = 99

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

2 x^{2} + 2 y^{2} - 20 y = 0

What is 4x^{(2)}+9y^{(2)}=2 ?
The solution to 4x^{(2)}+9y^{(2)}=2 is Ellipse with (h,k)=(0,0),a=sqrt(1/2),b=(sqrt(2))/3