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

The solution to 2x^2+x+y^2-6=0 is Ellipse with (h,k)=(-1/4 ,0),a= 7/4 ,b= 7/(2sqrt(2))

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

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

(h, k) = (- \frac{1}{4}, 0), a = \frac{7}{4}, b = \frac{7}{2 2}

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

\frac{( x - ( - \frac{1}{4} ) ) ^{2}}{( \frac{7}{4} ) ^{2}} + \frac{( y - 0 ) ^{2}}{( \frac{7}{2 2} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (- \frac{1}{4}, 0), a = \frac{7}{4}, b = \frac{7}{2 2}

b > a

therefore

b

is semi-major axis and

a

is semi-minor axis

Ellipse with center (h, k) = (- \frac{1}{4}, 0), b = \frac{7}{2 2}, a = \frac{7}{4}

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

y^{2} + 4 x^{2} + 24 x + 16 y = - 84

\frac{y ^{2}}{10} + \frac{x ^{2}}{6} = 1

x^{2} - 8 x + 2 y^{2} + 8 y = 20

x^{2} + 36 y^{2} - 24 x - 288 y + 611 = 0

What is 2x^2+x+y^2-6=0 ?
The solution to 2x^2+x+y^2-6=0 is Ellipse with (h,k)=(-1/4 ,0),a= 7/4 ,b= 7/(2sqrt(2))