What is 2(x-1)^2+3(y-2)^2=6 ?

The solution to 2(x-1)^2+3(y-2)^2=6 is Ellipse with (h,k)=(1,2),a=sqrt(3),b=sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2(x-1)^2+3(y-2)^2=6

2 (x - 1)^{2} + 3 (y - 2)^{2} = 6

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

Solution steps

2 (x - 1)^{2} + 3 (y - 2)^{2} = 6

Rewrite

2 (x - 1)^{2} + 3 (y - 2)^{2} = 6

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

10 - \frac{x ^{2}}{2} - y^{2} = x^{2} + 4 y^{2}

x^{2} + 1 - 2 x + 4 y^{2} + 16 y > 0

(x + 5)^{2} + 9 (y + 3)^{2} = 36

\frac{( x + 5 ) ^{2}}{4} + \frac{( y + 5 ) ^{2}}{25} = 1

x^{2} + 4 y^{2} = 15

What is 2(x-1)^2+3(y-2)^2=6 ?
The solution to 2(x-1)^2+3(y-2)^2=6 is Ellipse with (h,k)=(1,2),a=sqrt(3),b=sqrt(2)