What is 1/4 (x-2)^2-1/16 (y+7)^2=1 ?

The solution to 1/4 (x-2)^2-1/16 (y+7)^2=1 is Hyperbola with (h,k)=(2,-7),a=2,b=4

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1/4 (x-2)^2-1/16 (y+7)^2=1

\frac{1}{4} (x - 2)^{2} - \frac{1}{16} (y + 7)^{2} = 1

(h, k) = (2, - 7), a = 2, b = 4

Solution steps

\frac{1}{4} (x - 2)^{2} - \frac{1}{16} (y + 7)^{2} = 1

Rewrite

\frac{1}{4} (x - 2)^{2} - \frac{1}{16} (y + 7)^{2} = 1

in the form of a standard hyperbola equation

\frac{( x - 2 ) ^{2}}{2 ^{2}} - \frac{( y - ( - 7 ) ) ^{2}}{4 ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (2, - 7), a = 2, b = 4

10 x^{(2)} - 25 y^{(2)} = 100

5 x^{2} - 4 y^{2} + 40 x + 24 y + 24 = 0

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

x^{2} - 81 y^{2} = 81

y^{2} - 9 x^{2} - 8 y - 54 x - 81 = 0

What is 1/4 (x-2)^2-1/16 (y+7)^2=1 ?
The solution to 1/4 (x-2)^2-1/16 (y+7)^2=1 is Hyperbola with (h,k)=(2,-7),a=2,b=4