What is 2x^2+3y^2+8x+8y-3=0 ?

The solution to 2x^2+3y^2+8x+8y-3=0 is Ellipse with (h,k)=(-2,-4/3),a= 7/(sqrt(6)),b= 7/3

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2x^2+3y^2+8x+8y-3=0

2 x^{2} + 3 y^{2} + 8 x + 8 y - 3 = 0

(h, k) = (- 2, - \frac{4}{3}), a = \frac{7}{6}, b = \frac{7}{3}

Solution steps

2 x^{2} + 3 y^{2} + 8 x + 8 y - 3 = 0

Rewrite

2 x^{2} + 3 y^{2} + 8 x + 8 y - 3 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{7}{6} ) ^{2}} + \frac{( y - ( - \frac{4}{3} ) ) ^{2}}{( \frac{7}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - \frac{4}{3}), a = \frac{7}{6}, b = \frac{7}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, - \frac{4}{3}), a = \frac{7}{6}, b = \frac{7}{3}

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

9 x^{2} + y^{2} + 90 x - 4 y + 193 = 0

\frac{x ^{2}}{16} + \frac{x}{2} + \frac{y ^{2}}{4} + y + 1 = 0

9 x^{2} + 4 y^{2} - 27 x + 16 y - 119 = 0

x^{2} + 5 y^{2} + 2 x - 30 y + 36 = 0

What is 2x^2+3y^2+8x+8y-3=0 ?
The solution to 2x^2+3y^2+8x+8y-3=0 is Ellipse with (h,k)=(-2,-4/3),a= 7/(sqrt(6)),b= 7/3