What is 2x^2+y^2+10x+12y=-12 ?

The solution to 2x^2+y^2+10x+12y=-12 is Ellipse with (h,k)=(-5/2 ,-6),a=(sqrt(73))/2 ,b=sqrt(73/2)

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2x^2+y^2+10x+12y=-12

2 x^{2} + y^{2} + 10 x + 12 y = - 12

(h, k) = (- \frac{5}{2}, - 6), a = \frac{73}{2}, b = \frac{73}{2}

Solution steps

2 x^{2} + y^{2} + 10 x + 12 y = - 12

Rewrite

2 x^{2} + y^{2} + 10 x + 12 y = - 12

in the form of the standard ellipse equation

\frac{( x - ( - \frac{5}{2} ) ) ^{2}}{( \frac{73}{2} ) ^{2}} + \frac{( y - ( - 6 ) ) ^{2}}{( \frac{73}{2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{5}{2}, - 6), a = \frac{73}{2}, b = \frac{73}{2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{5}{2}, - 6), b = \frac{73}{2}, a = \frac{73}{2}

\frac{x ^{2}}{15} + \frac{y ^{2}}{4} = 1

5 x^{2} + y^{2} = 25

4 (x - 5)^{2} + 3 (y - 5)^{2} = 192

25 x^{2} + y^{2} = 1

\frac{( x - 1 ) ^{2}}{9} + \frac{( y + 5 ) ^{2}}{16} = 1

What is 2x^2+y^2+10x+12y=-12 ?
The solution to 2x^2+y^2+10x+12y=-12 is Ellipse with (h,k)=(-5/2 ,-6),a=(sqrt(73))/2 ,b=sqrt(73/2)