Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

Consider the standard form of each of the following options given, and note the hyperbola properties through that derivation -

`Standard Form - (\left(x-5\right)^2)/(\left(√(7)\right)^2)-(\left(y-\left(-5\right)\right)^2)/(3^2)=1,\\Properties - \left(h,\:k\right)=\left(5,\:-5\right),\:a=√(7),\:b=3\\`

Similarly we can note the properties of each of the other hyperbolas. They are all similar to one another, but only option C is correct. Almost all options are present with a conjugate axis of length 6, but only option c is broad enough to include the point ( 1, - 5 ) and ( 9, - 5 ) in a given radius.

Solution = Option C!