What is 2x^2+4y^2+14x+8y+16=0 ?

The solution to 2x^2+4y^2+14x+8y+16=0 is Ellipse with (h,k)=(-7/2 ,-1),a= 5/2 ,b= 5/(2sqrt(2))

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2x^2+4y^2+14x+8y+16=0

2 x^{2} + 4 y^{2} + 14 x + 8 y + 16 = 0

(h, k) = (- \frac{7}{2}, - 1), a = \frac{5}{2}, b = \frac{5}{2 2}

Solution steps

2 x^{2} + 4 y^{2} + 14 x + 8 y + 16 = 0

Rewrite

2 x^{2} + 4 y^{2} + 14 x + 8 y + 16 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{7}{2} ) ) ^{2}}{( \frac{5}{2} ) ^{2}} + \frac{( y - ( - 1 ) ) ^{2}}{( \frac{5}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{7}{2}, - 1), a = \frac{5}{2}, b = \frac{5}{2 2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- \frac{7}{2}, - 1), a = \frac{5}{2}, b = \frac{5}{2 2}

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

\frac{x ^{2}}{9} + \frac{( y - 3 ) ^{2}}{4} = 1

x^{2} + 4 y^{2} - 6 x + 16 y = 0

2 x^{2} + 4 y^{2} + 10 x + 10 y - 3 = 0

9 x^{2} + 25 y^{2} - 18 x + 200 y + 184 = 0

What is 2x^2+4y^2+14x+8y+16=0 ?
The solution to 2x^2+4y^2+14x+8y+16=0 is Ellipse with (h,k)=(-7/2 ,-1),a= 5/2 ,b= 5/(2sqrt(2))