What is 6x^2+y^2-12x+2y=1 ?

The solution to 6x^2+y^2-12x+2y=1 is Ellipse with (h,k)=(1,-1),a= 2/(sqrt(3)),b=2sqrt(2)

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6x^2+y^2-12x+2y=1

6 x^{2} + y^{2} - 12 x + 2 y = 1

(h, k) = (1, - 1), a = \frac{2}{3}, b = 22

Solution steps

6 x^{2} + y^{2} - 12 x + 2 y = 1

Rewrite

6 x^{2} + y^{2} - 12 x + 2 y = 1

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (1, - 1), a = \frac{2}{3}, b = 22

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (1, - 1), b = 22, a = \frac{2}{3}

(x - 5)^{2} + (y + 8)^{2} + (x - 3)^{2} - 98 = 0

5 x^{2} + 9 y^{2} + 30 x = 0

4 x^{2} + 7 y^{2} = 28

5 u^{2} - 4 \cdot u + v^{2} + 2 \cdot v = 0

3 x^{2} + 2 y^{2} - 6 x - 12 y + 15 = 0

What is 6x^2+y^2-12x+2y=1 ?
The solution to 6x^2+y^2-12x+2y=1 is Ellipse with (h,k)=(1,-1),a= 2/(sqrt(3)),b=2sqrt(2)