What is (y^2+3)/4-(x^2-1)/5 =1 ?

The solution to (y^2+3)/4-(x^2-1)/5 =1 is Hyperbola with (h,k)=(0,0),a=sqrt(1/5),b= 1/2

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(y^2+3)/4-(x^2-1)/5 =1

\frac{y ^{2} + 3}{4} - \frac{x ^{2} - 1}{5} = 1

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{2}

Solution steps

\frac{y ^{2} + 3}{4} - \frac{x ^{2} - 1}{5} = 1

Rewrite

\frac{y ^{2} + 3}{4} - \frac{x ^{2} - 1}{5} = 1

in the form of a standard hyperbola equation

\frac{( y - 0 ) ^{2}}{( \frac{1}{5} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{1}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, 0), a = \frac{1}{5}, b = \frac{1}{2}

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

25 x^{2} - 9 y^{2} - 54 y = 306

16 x^{2} - 9 y^{2} - 96 x + 9 y - 36 = 0

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

x^{2} - 8 y^{2} - 6 x - 22 y + 4 = 0

What is (y^2+3)/4-(x^2-1)/5 =1 ?
The solution to (y^2+3)/4-(x^2-1)/5 =1 is Hyperbola with (h,k)=(0,0),a=sqrt(1/5),b= 1/2