What is ((y+2)^2}{12}+\frac{x^2)/2-1=0 ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

((y+2)^2}{12}+\frac{x^2)/2-1=0

\frac{( y + 2 ) ^{2}}{12} + \frac{x ^{2}}{2} - 1 = 0

(h, k) = (0, - 2), a = 2, b = 23

Solution steps

\frac{( y + 2 ) ^{2}}{12} + \frac{x ^{2}}{2} - 1 = 0

Rewrite

\frac{( y + 2 ) ^{2}}{12} + \frac{x ^{2}}{2} - 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (0, - 2), a = 2, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (0, - 2), b = 23, a = 2

x^{2} - x + 4 y^{2} + 24 y + 30 = 4

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

\frac{x ^{2}}{a ^{2}} + \frac{y ^{2}}{a - 16} = 1

5 x^{2} + 9 y^{2} - 8 x - 4 = 0

\frac{x ^{2}}{2} + \frac{y ^{2}}{4} = 1

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