What is 3x^2+4y^2+12x-8y+9=0 ?

The solution to 3x^2+4y^2+12x-8y+9=0 is Ellipse with (h,k)=(-2,1),a=sqrt(7/3),b=(sqrt(7))/2

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3x^2+4y^2+12x-8y+9=0

3 x^{2} + 4 y^{2} + 12 x - 8 y + 9 = 0

(h, k) = (- 2, 1), a = \frac{7}{3}, b = \frac{7}{2}

Solution steps

3 x^{2} + 4 y^{2} + 12 x - 8 y + 9 = 0

Rewrite

3 x^{2} + 4 y^{2} + 12 x - 8 y + 9 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 2, 1), a = \frac{7}{3}, b = \frac{7}{2}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (- 2, 1), a = \frac{7}{3}, b = \frac{7}{2}

3 x^{2} + 5 y^{2} - 6 x + 8 y - 7 = 0

\frac{x ^{2}}{16} + \frac{( y - 4 ) ^{2}}{1} = 1

5 x^{2} + 9 y^{2} = 81

\frac{x ^{2}}{45} + \frac{y ^{2}}{49} = 1

2 x^{2} + 2 y^{2} + 16 y = 0

What is 3x^2+4y^2+12x-8y+9=0 ?
The solution to 3x^2+4y^2+12x-8y+9=0 is Ellipse with (h,k)=(-2,1),a=sqrt(7/3),b=(sqrt(7))/2