What is 3x^2+y^2+20x+32=0 ?

The solution to 3x^2+y^2+20x+32=0 is Ellipse with (h,k)=(-10/3 ,0),a= 2/3 ,b= 2/(sqrt(3))

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3x^2+y^2+20x+32=0

3 x^{2} + y^{2} + 20 x + 32 = 0

(h, k) = (- \frac{10}{3}, 0), a = \frac{2}{3}, b = \frac{2}{3}

Solution steps

3 x^{2} + y^{2} + 20 x + 32 = 0

Rewrite

3 x^{2} + y^{2} + 20 x + 32 = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{10}{3} ) ) ^{2}}{( \frac{2}{3} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{2}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{10}{3}, 0), a = \frac{2}{3}, b = \frac{2}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{10}{3}, 0), b = \frac{2}{3}, a = \frac{2}{3}

y^{2} = 1 - 2 x^{2}

x^{2} + 2 z^{2} + 6 x - 8 z + 1 = 0

9 x^{2} + 5 y^{2} - 18 x - 20 y - 151 = 0

\frac{x ^{2}}{4} + \frac{( y - 5 ) ^{2}}{5} = 1

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

What is 3x^2+y^2+20x+32=0 ?
The solution to 3x^2+y^2+20x+32=0 is Ellipse with (h,k)=(-10/3 ,0),a= 2/3 ,b= 2/(sqrt(3))