What is 3x^2+2y^2+6x-4y+5=18 ?

The solution to 3x^2+2y^2+6x-4y+5=18 is Ellipse with (h,k)=(-1,1),a=sqrt(6),b=3

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3x^2+2y^2+6x-4y+5=18

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

(h, k) = (- 1, 1), a = 6, b = 3

Solution steps

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

Rewrite

3 x^{2} + 2 y^{2} + 6 x - 4 y + 5 = 18

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (- 1, 1), a = 6, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- 1, 1), b = 3, a = 6

f (x) = x^{2} + 8 x + 15

y^{2} = - 20 x

f (x) = - \frac{x ^{2}}{10} + \frac{9 x}{10} + \frac{11}{5}

y^{2} = 32 x

y + 4 x \leq x^{2} + 2

What is 3x^2+2y^2+6x-4y+5=18 ?
The solution to 3x^2+2y^2+6x-4y+5=18 is Ellipse with (h,k)=(-1,1),a=sqrt(6),b=3