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

The solution to 2x^2+y^2+6x-2y-10=0 is Ellipse with (h,k)=(-3/2 ,1),a=(sqrt(31))/2 ,b=sqrt(31/2)

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

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

(h, k) = (- \frac{3}{2}, 1), a = \frac{31}{2}, b = \frac{31}{2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - \frac{3}{2} ) ) ^{2}}{( \frac{31}{2} ) ^{2}} + \frac{( y - 1 ) ^{2}}{( \frac{31}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{3}{2}, 1), a = \frac{31}{2}, b = \frac{31}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{3}{2}, 1), b = \frac{31}{2}, a = \frac{31}{2}

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

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

\frac{( y - 3 ) ^{2}}{16} + \frac{( x + 2 ) ^{2}}{9} = 1

7 (x - 2004)^{2} = 23 - y^{2}

\frac{( x - 6 ) ^{2}}{25} + \frac{( y - 7 ) ^{2}}{9} = 1

What is 2x^2+y^2+6x-2y-10=0 ?
The solution to 2x^2+y^2+6x-2y-10=0 is Ellipse with (h,k)=(-3/2 ,1),a=(sqrt(31))/2 ,b=sqrt(31/2)