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

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

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

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

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

Solution steps

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

Rewrite

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

in the form of the standard ellipse equation

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

Therefore ellipse properties are:

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

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

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

\frac{( x - 23 ) ^{2}}{841} + \frac{( y + 28 ) ^{2}}{484} = 1

3 x^{2} - 12 x + 2 y^{2} + 8 y + 14 = 0

(x - 7)^{2} + 6 y^{2} + 12 y = 0

4 x^{2} + 5 y^{2} = 445

\frac{x ^{2}}{25} + \frac{y ^{2}}{b ^{2}} = 1

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