What is 2x^2+3y^2+8x+8y-10=0 ?

The solution to 2x^2+3y^2+8x+8y-10=0 is Ellipse with (h,k)=(-2,-4/3),a=sqrt(35/3),b=(sqrt(70))/3

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2x^2+3y^2+8x+8y-10=0

2 x^{2} + 3 y^{2} + 8 x + 8 y - 10 = 0

(h, k) = (- 2, - \frac{4}{3}), a = \frac{35}{3}, b = \frac{70}{3}

Solution steps

2 x^{2} + 3 y^{2} + 8 x + 8 y - 10 = 0

Rewrite

2 x^{2} + 3 y^{2} + 8 x + 8 y - 10 = 0

in the form of the standard ellipse equation

\frac{( x - ( - 2 ) ) ^{2}}{( \frac{35}{3} ) ^{2}} + \frac{( y - ( - \frac{4}{3} ) ) ^{2}}{( \frac{70}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 2, - \frac{4}{3}), a = \frac{35}{3}, b = \frac{70}{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{35}{3}, b = \frac{70}{3}

What is 2x^2+3y^2+8x+8y-10=0 ?
The solution to 2x^2+3y^2+8x+8y-10=0 is Ellipse with (h,k)=(-2,-4/3),a=sqrt(35/3),b=(sqrt(70))/3