What is y^2+2x^2-2y+4x-6=0 ?

The solution to y^2+2x^2-2y+4x-6=0 is Ellipse with (h,k)=(-1,1),a= 3/(sqrt(2)),b=3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^2+2x^2-2y+4x-6=0

y^{2} + 2 x^{2} - 2 y + 4 x - 6 = 0

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

Solution steps

y^{2} + 2 x^{2} - 2 y + 4 x - 6 = 0

Rewrite

y^{2} + 2 x^{2} - 2 y + 4 x - 6 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

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

x^{2} + 3 y^{2} - 6 x + 6 y = 0

2 x^{2} + y^{2} = 50

9 x^{2} + 5 y^{2} + 18 x + 10 y - 31 = 0

x^{2} + 5 y^{2} + 10 y + 4 x - 27 = 0

x^{2} + 4 y^{2} \geq 100

What is y^2+2x^2-2y+4x-6=0 ?
The solution to y^2+2x^2-2y+4x-6=0 is Ellipse with (h,k)=(-1,1),a= 3/(sqrt(2)),b=3