What is y^2-5x^2+20x=50 ?

The solution to y^2-5x^2+20x=50 is Hyperbola with (h,k)=(2,0),a=sqrt(30),b=sqrt(6)

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y^2-5x^2+20x=50

y^{2} - 5 x^{2} + 20 x = 50

(h, k) = (2, 0), a = 30, b = 6

Solution steps

y^{2} - 5 x^{2} + 20 x = 50

Rewrite

y^{2} - 5 x^{2} + 20 x = 50

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( 30 ) ^{2}} - \frac{( x - 2 ) ^{2}}{( 6 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, 0), a = 30, b = 6

\frac{( y + 2 ) ^{2}}{9} - \frac{( x + 4 ) ^{2}}{40} = 1

4 x^{2} - 9 y^{2} + 24 x + 18 y - 9 = 0

2 x^{2} - 3 y^{2} < 1

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

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

What is y^2-5x^2+20x=50 ?
The solution to y^2-5x^2+20x=50 is Hyperbola with (h,k)=(2,0),a=sqrt(30),b=sqrt(6)