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

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

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

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

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

Solution steps

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

Rewrite

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

x^{2} + 4 y^{2} - 4 \geq 0

2 x^{2} + 3 y^{2} - 6 x + 4 - y = 0

- 5 x^{2} - 5 y^{2} + x - 2 y - 10 = 0

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

9 x^{2} + 8 y^{2} = 72

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