Question

Which is the graph of the following equation?

Answer 1

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

Answer 2

Given equation is

`((x-5)^2)/(16) - ((y-2)^2)/(9)=1`

The given equation is in the form of

`((x-h)^2)/(a^2) - ((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