What is (x-1)^2-(y-10)^2=-40 ?

The solution to (x-1)^2-(y-10)^2=-40 is Hyperbola with (h,k)=(1,10),a=2sqrt(10),b=2sqrt(10)

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(x-1)^2-(y-10)^2=-40

(x - 1)^{2} - (y - 10)^{2} = - 40

(h, k) = (1, 10), a = 210, b = 210

Solution steps

(x - 1)^{2} - (y - 10)^{2} = - 40

Rewrite

(x - 1)^{2} - (y - 10)^{2} = - 40

in the form of a standard hyperbola equation

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

Therefore Hyperbola properties are:

(h, k) = (1, 10), a = 210, b = 210

\frac{( y + 9 ) ^{2}}{49} - \frac{( x - 1 ) ^{2}}{9} = 1

y^{2} + 7 = x^{2} - 8

\frac{( a ^{2} + b ^{2} )}{2} - 2 (a^{2} - b^{2}) = - 15

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

\frac{( y + 5 ) ^{2}}{25} - \frac{( x - 6 ) ^{2}}{16} = 1

What is (x-1)^2-(y-10)^2=-40 ?
The solution to (x-1)^2-(y-10)^2=-40 is Hyperbola with (h,k)=(1,10),a=2sqrt(10),b=2sqrt(10)