What is 0=y^2-y-(x^2)/4+24 ?

The solution to 0=y^2-y-(x^2)/4+24 is Hyperbola with (h,k)=(0, 1/2),a=sqrt(95),b=(sqrt(95))/2

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0=y^2-y-(x^2)/4+24

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

(h, k) = (0, \frac{1}{2}), a = 95, b = \frac{95}{2}

Solution steps

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

Rewrite

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

in the form of a standard hyperbola equation

\frac{( x - 0 ) ^{2}}{( 95 ) ^{2}} - \frac{( y - \frac{1}{2} ) ^{2}}{( \frac{95}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, \frac{1}{2}), a = 95, b = \frac{95}{2}

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

\frac{x ^{2}}{16} - \frac{y ^{2}}{7} = 1

\frac{x ^{2}}{64} - \frac{y ^{2}}{81} = 1

(x^{2} - 4 x + 4) - (y^{2} - 6 y + 9) = 9

a^{2} + 150 = b^{2} + 9

What is 0=y^2-y-(x^2)/4+24 ?
The solution to 0=y^2-y-(x^2)/4+24 is Hyperbola with (h,k)=(0, 1/2),a=sqrt(95),b=(sqrt(95))/2