Find the vertices and locate the foci for the hyperbola whos

Find the vertices and locate the foci for the hyperbola whose equation is given.

49x² - 100y² = 4900

49x2 - 100y2 = 4900

Divide by 4900 all over :

x^2/100 - y^2/49 = 1

This is of the form
x^2/a^2 - y^2/b^2 = 1

So, we have center (h,k) = (0,0)
and a = 10 and b = 7

With this, knowing that for hyperbola
c = sqrt(a^2 + b ^2), we have
c = sqrt(149)

Now, this is a horizontal hyperboal centered at the origin
so its foci are given by :
foci: (h + c, k), (h - c, k)

Since center = (0,0), we have :
foci : (c,0) and (-c,0)

And thus
(sqrt149, 0 )
and
(-sqrt149 , 0)

Now, vertices :
vertices: (h + a, k), (h - a, k) for horizontal hyperbola
With (h,k) = (0,0) :
vertices = (a,0) and (-a,0)

And thus vertices are (10,0) and (-10,0)

Thus, option B