What is (y+2)^2-x^2+y-9=0 ?

The solution to (y+2)^2-x^2+y-9=0 is Hyperbola with (h,k)=(0,-5/2),a=(3sqrt(5))/2 ,b=(3sqrt(5))/2

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(y+2)^2-x^2+y-9=0

(y + 2)^{2} - x^{2} + y - 9 = 0

(h, k) = (0, - \frac{5}{2}), a = \frac{3 5}{2}, b = \frac{3 5}{2}

Solution steps

(y + 2)^{2} - x^{2} + y - 9 = 0

Rewrite

(y + 2)^{2} - x^{2} + y - 9 = 0

in the form of a standard hyperbola equation

\frac{( y - ( - \frac{5}{2} ) ) ^{2}}{( \frac{3 5}{2} ) ^{2}} - \frac{( x - 0 ) ^{2}}{( \frac{3 5}{2} ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (0, - \frac{5}{2}), a = \frac{3 5}{2}, b = \frac{3 5}{2}

9 x^{2} - y^{2} - 36 x - 6 y + 36 = 0

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

yy = x^{2} - 2 x

36 x^{2} - 64 y^{2} - 504 x + 768 y - 2844 = 0

4 x^{2} - 5 y^{2} + 8 x - 10 y + 19 = 0

What is (y+2)^2-x^2+y-9=0 ?
The solution to (y+2)^2-x^2+y-9=0 is Hyperbola with (h,k)=(0,-5/2),a=(3sqrt(5))/2 ,b=(3sqrt(5))/2