Question

Which is the graph of the following equation?

Answer 1

Given equation is

$\frac{(x-5)^2}{16} - \frac{(y-2)^2}{9}=1$

The given equation is in the form of

$\frac{(x-h)^2}{a^2} - \frac{(y-k)^2}{b^2}=1$

a^2= 16  , so a=4

b^2 = 9 so b= 4

The value of 'a' is greater than the value of 'b'

So it is a Horizontal hyperbola

First two graphs are horizontal hyperbola

Here center is (h,k)  

h= 5 and k =2 from the given equation

So center is (5,2)

Now we find vertices

Vertices are (h+a,k)  and (h-a,k)

We know h=5, k=2  and a=4

So vertices are (9,2)  and (1,2)

Second graph having same vertices and center

The correct graph is attached below

Answer 2

Answer:

Graph B is the correct choice out of all of them !