What is -2p^2+2q+p=3q^2+q-3p-2 ?

The solution to -2p^2+2q+p=3q^2+q-3p-2 is Ellipse with (h,k)=(1, 1/6),a= 7/(2sqrt(6)),b= 7/6

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-2p^2+2q+p=3q^2+q-3p-2

- 2 p^{2} + 2 q + p = 3 q^{2} + q - 3 p - 2

(h, k) = (1, \frac{1}{6}), a = \frac{7}{2 6}, b = \frac{7}{6}

Solution steps

- 2 p^{2} + 2 q + p = 3 q^{2} + q - 3 p - 2

Rewrite

- 2 p^{2} + 2 q + p - 3 q^{2} - q + 3 p + 2 = 0

in the form of the standard ellipse equation

\frac{( p - 1 ) ^{2}}{( \frac{7}{2 6} ) ^{2}} + \frac{( q - \frac{1}{6} ) ^{2}}{( \frac{7}{6} ) ^{2}} = 1

Therefore ellipse properties are:

(h, k) = (1, \frac{1}{6}), a = \frac{7}{2 6}, b = \frac{7}{6}

a > b

therefore

a

is semi-major axis and

b

is semi-minor axis

Ellipse with center (h, k) = (1, \frac{1}{6}), a = \frac{7}{2 6}, b = \frac{7}{6}

2 X^{2} - 6 < - 6 Y^{2}

4 x^{2} + y^{2} + 8 x + 2 y - 31 = 0

4 x^{2} + 3 y^{2} - 8 x + 12 y - 32 = 0

x^{2} + 4 y^{2} - 6 x - 55 = 0

9 x^{2} + 4 y^{2} + 36 x + 16 y + 16 = 0

What is -2p^2+2q+p=3q^2+q-3p-2 ?
The solution to -2p^2+2q+p=3q^2+q-3p-2 is Ellipse with (h,k)=(1, 1/6),a= 7/(2sqrt(6)),b= 7/6