What is x^2+2y^2+2x-4y-1=0 ?

The solution to x^2+2y^2+2x-4y-1=0 is Ellipse with (h,k)=(-1,1),a=2,b=sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

x^2+2y^2+2x-4y-1=0

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

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

Solution steps

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

Rewrite

x^{2} + 2 y^{2} + 2 x - 4 y - 1 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + y^{2} - 36 x + 120 y + 80 = 0

- 2 p^{2} + 2 q + p = 3 q^{2} + q - 3 p - 2

2 X^{2} - 6 < - 6 Y^{2}

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

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