What is 6x^2+2y^2+18x-10y+2=0 ?

The solution to 6x^2+2y^2+18x-10y+2=0 is Ellipse with (h,k)=(-3/2 , 5/2),a=2,b=2sqrt(3)

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6x^2+2y^2+18x-10y+2=0

6 x^{2} + 2 y^{2} + 18 x - 10 y + 2 = 0

(h, k) = (- \frac{3}{2}, \frac{5}{2}), a = 2, b = 23

Solution steps

6 x^{2} + 2 y^{2} + 18 x - 10 y + 2 = 0

Rewrite

6 x^{2} + 2 y^{2} + 18 x - 10 y + 2 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{3}{2} ) ) ^{2}}{2 ^{2}} + \frac{( y - \frac{5}{2} ) ^{2}}{( 2 3 ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{3}{2}, \frac{5}{2}), a = 2, b = 23

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{3}{2}, \frac{5}{2}), b = 23, a = 2

16 x^{2} + 9 y^{2} - 128 x - 18 y + 121 = 0

\frac{( x - 2 ) ^{2}}{9} + \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{4} + \frac{y ^{2}}{36} = 1

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

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

What is 6x^2+2y^2+18x-10y+2=0 ?
The solution to 6x^2+2y^2+18x-10y+2=0 is Ellipse with (h,k)=(-3/2 , 5/2),a=2,b=2sqrt(3)