Question

Which of the following is false for the hyperbola (x+5)^2/4^2 - (y-2)^2/3^2=1

A)The transverse axis is horizontal
B)one of the foci has coordinates (0,2)
C)One of the vertices is (-10,2)
D)The center is at (-5,2)

Answer 1

C)One of the vertices is (-10,2)

Explanation:

Given the hyperbola:
`((x+5)^2)/(4^2) -( (y-2)^2)/(3^2) =1`

The standard equation for a hyperbola with a horizontal transverse axis is:

`((x-h)^2)/(a^2) -( (y-k)^2)/(b^2) =1` where the center is at (h, k).

For our given hyperbola, the center (h,k)=(-5,2)

Now:

`c^2=a^2+b^2\\c^2=4^2+3^2\\c^2=25\\c=5`

Since the center is at (-5,2), its foci (-c,0) and (c,0) are:

(-5-5,2) and (-5+5,2)= (-10,2) and (0,2)

Similarly, since the center is at (-5,2), its vertices, (-a,0) and (a,0) are:

(-5-4,2) and (-5+4,2)= (−9,2), (−1,2).

Therefore, the odd option is C.