What is 3x^2-12x+2y^2+8y+14=0 ?

The solution to 3x^2-12x+2y^2+8y+14=0 is Ellipse with (h,k)=(2,-2),a=sqrt(2),b=sqrt(3)

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3x^2-12x+2y^2+8y+14=0

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

(h, k) = (2, - 2), a = 2, b = 3

Solution steps

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

Rewrite

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

(h, k) = (2, - 2), a = 2, b = 3

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (2, - 2), b = 3, a = 2

(x - 7)^{2} + 6 y^{2} + 12 y = 0

4 x^{2} + 5 y^{2} = 445

\frac{x ^{2}}{25} + \frac{y ^{2}}{b ^{2}} = 1

Y, 2 x^{2} - 6 < - 6 Y (x)^{2}

(\frac{x + 2}{4})^{2} + (\frac{y - 3}{16})^{2} = 1

What is 3x^2-12x+2y^2+8y+14=0 ?
The solution to 3x^2-12x+2y^2+8y+14=0 is Ellipse with (h,k)=(2,-2),a=sqrt(2),b=sqrt(3)