What is 6x^2+10x+y^2=0 ?

The solution to 6x^2+10x+y^2=0 is Ellipse with (h,k)=(-5/6 ,0),a= 5/6 ,b= 5/(sqrt(6))

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6x^2+10x+y^2=0

6 x^{2} + 10 x + y^{2} = 0

(h, k) = (- \frac{5}{6}, 0), a = \frac{5}{6}, b = \frac{5}{6}

Solution steps

6 x^{2} + 10 x + y^{2} = 0

Rewrite

6 x^{2} + 10 x + y^{2} = 0

in the form of the standard ellipse equation

\frac{( x - ( - \frac{5}{6} ) ) ^{2}}{( \frac{5}{6} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{5}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{5}{6}, 0), a = \frac{5}{6}, b = \frac{5}{6}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{5}{6}, 0), b = \frac{5}{6}, a = \frac{5}{6}

27 x^{2} - 54 x + 48 y^{2} - 192 y - 213 = 0

\frac{( x - 5 ) ^{2}}{4} + \frac{( y - 4 ) ^{2}}{16} = 1

\frac{( x + 2 ) ^{2}}{16} + \frac{( y - 2 ) ^{2}}{9} = 1

\frac{( x + 3 ) ^{2}}{4} + \frac{4 y ^{2}}{9} = 1

9 x^{(2)} + 4 y^{(2)} + 36 x - 24 y + 36 = 0

What is 6x^2+10x+y^2=0 ?
The solution to 6x^2+10x+y^2=0 is Ellipse with (h,k)=(-5/6 ,0),a= 5/6 ,b= 5/(sqrt(6))