What is x^2-x-4y^2+24y-35=0 ?

The solution to x^2-x-4y^2+24y-35=0 is Hyperbola with (h,k)=(1/2 ,3),a=(sqrt(3))/4 ,b=(sqrt(3))/2

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x^2-x-4y^2+24y-35=0

x^{2} - x - 4 y^{2} + 24 y - 35 = 0

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

Solution steps

x^{2} - x - 4 y^{2} + 24 y - 35 = 0

Rewrite

x^{2} - x - 4 y^{2} + 24 y - 35 = 0

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

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

x^{2} - y^{2} + 16 = 0

y^{2} = x^{2} + 12

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

x^{2} \frac{1}{4} - y^{2} \frac{1}{9} = 1

(x - 1)^{2} - (y + 1)^{2} = 1

What is x^2-x-4y^2+24y-35=0 ?
The solution to x^2-x-4y^2+24y-35=0 is Hyperbola with (h,k)=(1/2 ,3),a=(sqrt(3))/4 ,b=(sqrt(3))/2