What is x-y=-3x^2+2y^2 ?

The solution to x-y=-3x^2+2y^2 is Hyperbola with (h,k)=(-1/6 ,-1/4),a= 1/(4sqrt(3)),b= 1/(6sqrt(2))

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x-y=-3x^2+2y^2

x - y = - 3 x^{2} + 2 y^{2}

(h, k) = (- \frac{1}{6}, - \frac{1}{4}), a = \frac{1}{4 3}, b = \frac{1}{6 2}

Solution steps

x - y = - 3 x^{2} + 2 y^{2}

Rewrite

x - y = - 3 x^{2} + 2 y^{2}

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{1}{4} ) ) ^{2}}{( \frac{1}{4 3} ) ^{2}} - \frac{( x - ( - \frac{1}{6} ) ) ^{2}}{( \frac{1}{6 2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- \frac{1}{6}, - \frac{1}{4}), a = \frac{1}{4 3}, b = \frac{1}{6 2}

\frac{y - 3}{x - 3} - \frac{2 x + 1}{y + 1} = 0

x^{2} - y^{2} - 8 x - 14 y - 49 = 0

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

[f (x)]^{2} = 2 x^{2} - x + 5

\frac{( x + 4 ) ^{2}}{64} - \frac{( y + 5 ) ^{2}}{81} = 1

What is x-y=-3x^2+2y^2 ?
The solution to x-y=-3x^2+2y^2 is Hyperbola with (h,k)=(-1/6 ,-1/4),a= 1/(4sqrt(3)),b= 1/(6sqrt(2))