What is 3x^2+y^2+2x-6y-3=0 ?

The solution to 3x^2+y^2+2x-6y-3=0 is Ellipse with (h,k)=(-1/3 ,3),a=(sqrt(37))/3 ,b=sqrt(37/3)

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3x^2+y^2+2x-6y-3=0

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

(h, k) = (- \frac{1}{3}, 3), a = \frac{37}{3}, b = \frac{37}{3}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - \frac{1}{3} ) ) ^{2}}{( \frac{37}{3} ) ^{2}} + \frac{( y - 3 ) ^{2}}{( \frac{37}{3} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{1}{3}, 3), a = \frac{37}{3}, b = \frac{37}{3}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{1}{3}, 3), b = \frac{37}{3}, a = \frac{37}{3}

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

25 x^{2} + 4 y^{2} - 50 x + 16 y - 59 = 0

5 x^{2} + 7 y^{2} = 35

(\frac{x ^{2}}{a}) + (\frac{y ^{2}}{b}) = 1

\frac{( x - 10 ) ^{2}}{25} + \frac{( y - 4 ) ^{2}}{36} = 1

What is 3x^2+y^2+2x-6y-3=0 ?
The solution to 3x^2+y^2+2x-6y-3=0 is Ellipse with (h,k)=(-1/3 ,3),a=(sqrt(37))/3 ,b=sqrt(37/3)