If the line y=mx+c  is a common tangent to the hyperbola x2100−y264=1 and the circle x2+y2=36, then which one of the following is true?

If  y = mx + c is a tangent to x2102−y282=1, then∴        c2=100m2−64                                   …(i)y=mx+c is also tangent for x2+y2=36 ,then c2=361+m2→iiFrom (i) and (ii), we obtain 100m2−64=361+m2⇒64m2=100⇒m=±54∴ c2=361+2516=3694             Putting m=±54 in (ii) ⇒4c2=369