What is ((x-3)^2}{10}-\frac{(y+5)^2)/9 =4 ?

The solution to ((x-3)^2}{10}-\frac{(y+5)^2)/9 =4 is Hyperbola with (h,k)=(3,-5),a=2sqrt(10),b=6

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((x-3)^2}{10}-\frac{(y+5)^2)/9 =4

\frac{( x - 3 ) ^{2}}{10} - \frac{( y + 5 ) ^{2}}{9} = 4

(h, k) = (3, - 5), a = 210, b = 6

Solution steps

\frac{( x - 3 ) ^{2}}{10} - \frac{( y + 5 ) ^{2}}{9} = 4

Rewrite

\frac{( x - 3 ) ^{2}}{10} - \frac{( y + 5 ) ^{2}}{9} = 4

in the form of a standard hyperbola equation

\frac{( x - 3 ) ^{2}}{( 2 10 ) ^{2}} - \frac{( y - ( - 5 ) ) ^{2}}{6 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (3, - 5), a = 210, b = 6

x, 12 Y (x)^{2} - 15 x^{2} = 180

9 x^{2} - 16 y^{2} - 90 x - 96 y - 63 = 0

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

x^{2} - 9 (y + 1)^{2} - 9 = x + 2 y + 5

- 16 x^{2} + 25 y^{2} - 32 x + 100 y = 316

What is ((x-3)^2}{10}-\frac{(y+5)^2)/9 =4 ?
The solution to ((x-3)^2}{10}-\frac{(y+5)^2)/9 =4 is Hyperbola with (h,k)=(3,-5),a=2sqrt(10),b=6