What is 8x^2+9y^2+24x+12y+10=0 ?

The solution to 8x^2+9y^2+24x+12y+10=0 is Ellipse with (h,k)=(-3/2 ,-2/3),a=sqrt(3/2),b= 2/(sqrt(3))

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8x^2+9y^2+24x+12y+10=0

8 x^{2} + 9 y^{2} + 24 x + 12 y + 10 = 0

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

Solution steps

8 x^{2} + 9 y^{2} + 24 x + 12 y + 10 = 0

Rewrite

8 x^{2} + 9 y^{2} + 24 x + 12 y + 10 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

4 x^{2} + y^{2} - 8 x - 6 y - 3 = 0

5 x^{(2)} + 9 y^{(2)} = 180

5 x^{2} + 4 y^{2} = 56

25 x^{2} + 9 y^{2} - 100 y + 18 x - 116 = 0

2 x^{2} + 3 y^{2} + 4 x - 5 y - 6 = 0

What is 8x^2+9y^2+24x+12y+10=0 ?
The solution to 8x^2+9y^2+24x+12y+10=0 is Ellipse with (h,k)=(-3/2 ,-2/3),a=sqrt(3/2),b= 2/(sqrt(3))