Which foci belong to the hyperbola represented by the equation

The foci belong to the hyperbola represented by the equation:

(x-14)^2/16^2-(y-2)^2/30^2=1 are:

Option A. (-20,2) and (48,2)

Step-by-step explanation:

The equation (x-14)^2/16^2-(y-2)^2/30^2=1 has the form:

(x-h)^2/a^2-(y-k)^2/b^2=1

And the coordinates of the foci are (h-c,k) and (h+c,k)

Comparing with the form:

h=14

k=2

a^2=16^2

b^2=30^2

c^2=a^2+b^2→c^2=16^2+30^2→c^2=256+900→c^2=1,156→

sqrt(c^2)=sqrt(1,156)→c=34

Then the coordinates of the foci are:

(h-c,k)=(14-34,2)→(h-c,k)=(-20,2)

(h+c,k)=(14+34,2)→(h+c,k)=(48,2)

The coordnates of the foci are (-20,2) and (48,2)

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