What is x^2+3y^2-12y+9=0 ?

The solution to x^2+3y^2-12y+9=0 is Ellipse with (h,k)=(0,2),a=sqrt(3),b=1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2+3y^2-12y+9=0

x^{2} + 3 y^{2} - 12 y + 9 = 0

(h, k) = (0, 2), a = 3, b = 1

Solution steps

x^{2} + 3 y^{2} - 12 y + 9 = 0

Rewrite

x^{2} + 3 y^{2} - 12 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, 2), a = 3, b = 1

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (0, 2), a = 3, b = 1

4 x^{2} + 9 y^{2} - 40 x + 36 y + 100 = 0

\frac{( x - 8 ) ^{2}}{64} + \frac{( y - 5 ) ^{2}}{5 ^{2}} = 1

x^{2} + 3 y^{2} = 7

\frac{( x - 8 ) ^{2}}{49} + \frac{( y + 5 ) ^{2}}{9} = 1

\frac{( x - 42 ) ^{2}}{12} + \frac{( y - 20 ) ^{2}}{27} = 1

What is x^2+3y^2-12y+9=0 ?
The solution to x^2+3y^2-12y+9=0 is Ellipse with (h,k)=(0,2),a=sqrt(3),b=1