What is 9(y+3)^2-1(x+2)^2=15 ?

The solution to 9(y+3)^2-1(x+2)^2=15 is Hyperbola with (h,k)=(-2,-3),a=sqrt(5/3),b=sqrt(15)

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9(y+3)^2-1(x+2)^2=15

9 (y + 3)^{2} - 1 (x + 2)^{2} = 15

(h, k) = (- 2, - 3), a = \frac{5}{3}, b = 15

Solution steps

9 (y + 3)^{2} - 1 \cdot (x + 2)^{2} = 15

Rewrite

9 (y + 3)^{2} - 1 (x + 2)^{2} = 15

in the form of a standard hyperbola equation

\frac{( y - ( - 3 ) ) ^{2}}{( \frac{5}{3} ) ^{2}} - \frac{( x - ( - 2 ) ) ^{2}}{( 15 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (- 2, - 3), a = \frac{5}{3}, b = 15

\frac{y ^{2}}{64} - \frac{x ^{2}}{16} = 1

\frac{( x - 4 ) ^{2}}{16} - \frac{( y + 5 ) ^{2}}{25} = 1

4 x^{2} - 3 y^{2} + 5 y - 6 y + 2 x = 7

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

y^{2} - x^{2} = 121

What is 9(y+3)^2-1(x+2)^2=15 ?
The solution to 9(y+3)^2-1(x+2)^2=15 is Hyperbola with (h,k)=(-2,-3),a=sqrt(5/3),b=sqrt(15)