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)

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

Step-by-step explanation:

Given the hyperbola:

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

where the center is at (h, k).

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

Now:

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.

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.