we use a tool to graph
[tex]\frac{\left(x-1\right)^2}{9}-\frac{\left(y-5\right)^2}{25}=1[/tex]
now find the value of c, c is the distance between foci and find it using
[tex]c=\sqrt[]{a^2+b^2}[/tex]
where a and b are the roots of the denominator on the original function
a=3 and b=5
[tex]\begin{gathered} c=\sqrt[]{3^2+5^2} \\ c=\sqrt[]{34} \end{gathered}[/tex]
the parabola is moved to right 1 unit then we need to add 1 to the measure
[tex]c=1\pm\sqrt[]{34}[/tex]
we have two solutions for c because we have 2 foci
the general form of the foci points on this exercise is
[tex](c,5)[/tex]
y is 5 because it is the transversal axis of the function now replace the two values of c to find the foci
[tex]\begin{gathered} (1+\sqrt[]{34},5) \\ (1-\sqrt[]{34},5) \end{gathered}[/tex]
then right option is the last
