What is y^2-4y=3x^2-10x ?

The solution to y^2-4y=3x^2-10x is Hyperbola with (h,k)=(5/3 ,2),a=(sqrt(13))/3 ,b=sqrt(13/3)

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y^2-4y=3x^2-10x

y^{2} - 4 y = 3 x^{2} - 10 x

(h, k) = (\frac{5}{3}, 2), a = \frac{13}{3}, b = \frac{13}{3}

Solution steps

y^{2} - 4 y = 3 x^{2} - 10 x

Rewrite

y^{2} - 4 y = 3 x^{2} - 10 x

in the form of a standard hyperbola equation

\frac{( x - \frac{5}{3} ) ^{2}}{( \frac{13}{3} ) ^{2}} - \frac{( y - 2 ) ^{2}}{( \frac{13}{3} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (\frac{5}{3}, 2), a = \frac{13}{3}, b = \frac{13}{3}

(\frac{a + b}{100}) \cdot (a - b) = \frac{1}{25}

x^{2} + 3 x - 2 y^{2} + y - 23 = 0

\frac{( y - 8 ) ^{2}}{4} - \frac{( x - 5 ) ^{2}}{9} = 1

4 x^{2} - y^{2} - 4 y - 40 = 0

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

What is y^2-4y=3x^2-10x ?
The solution to y^2-4y=3x^2-10x is Hyperbola with (h,k)=(5/3 ,2),a=(sqrt(13))/3 ,b=sqrt(13/3)