Question

For the following equation, find the foci of the hyperbola

Answer 1

we use a tool to graph

`(\left(x-1\right)^2)/(9)-(\left(y-5\right)^2)/(25)=1`

now find the value of c, c is the distance between foci and find it using

`c=\sqrt[]{a^2+b^2}`

where a and b are the roots of the denominator on the original function

a=3 and b=5

`\begin{gathered} c=\sqrt[]{3^2+5^2} \\ c=\sqrt[]{34} \end{gathered}`

the parabola is moved to right 1 unit then we need to add 1 to the measure

`c=1\pm\sqrt[]{34}`

we have two solutions for c because we have 2 foci

the general form of the foci points on this exercise is

`(c,5)`

y is 5 because it is the transversal axis of the function now replace the two values of c to find the foci

`\begin{gathered} (1+\sqrt[]{34},5) \\ (1-\sqrt[]{34},5) \end{gathered}`

then right option is the last