What is (x^2+8x)+(3y^2+8y)=11 ?

The solution to (x^2+8x)+(3y^2+8y)=11 is Ellipse with (h,k)=(-4,-4/3),a=sqrt(97/3),b=(sqrt(97))/3

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(x^2+8x)+(3y^2+8y)=11

(x^{2} + 8 x) + (3 y^{2} + 8 y) = 11

(h, k) = (- 4, - \frac{4}{3}), a = \frac{97}{3}, b = \frac{97}{3}

Solution steps

x^{2} + 8 x + (3 y^{2} + 8 y) = 11

Rewrite

x^{2} + 8 x + (3 y^{2} + 8 y) = 11

in the form of the standard ellipse equation

\frac{( x - ( - 4 ) ) ^{2}}{( \frac{97}{3} ) ^{2}} + \frac{( y - ( - \frac{4}{3} ) ) ^{2}}{( \frac{97}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- 4, - \frac{4}{3}), a = \frac{97}{3}, b = \frac{97}{3}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 4, - \frac{4}{3}), a = \frac{97}{3}, b = \frac{97}{3}

\frac{( x + 2 ) ^{2}}{20} + \frac{( y - 3 ) ^{2}}{4} = 1

- 4 x^{2} - 9 y^{2} + 8 x - 18 y + 23 = 0

\frac{16 x ^{2}}{144} + \frac{9 y ^{2}}{144} = 1

x^{2} + 3 y^{2} - 13 - y^{2} - 4 x = 0

2 x^{2} - 200 x + y^{2} + 4 y + 379 = 0

What is (x^2+8x)+(3y^2+8y)=11 ?
The solution to (x^2+8x)+(3y^2+8y)=11 is Ellipse with (h,k)=(-4,-4/3),a=sqrt(97/3),b=(sqrt(97))/3