Question

Answer Problems 9–11 using the figure.

If the center of the hyperbola is $(2,1)$and $c=5$, then the coordinates of the foci are ______ and _______ .

Short answer

If the centre of the hyperbola is $(2,1)$and $c=5$, then the

coordinates of the foci are$(2,6)$and$(2,-4)$

Step-by-step solution

Step 1. Given Information

The centre of the hyperbola is $(2,1)$and $c=5.$

Step 2. Aim of the problem

We need to find the coordinates of the foci.

Step 3. Concept

Foci$=(h,k\pm c)$, when the transverse axis is parallel to the $y-$axis and the centre of the hyperbola is $(h,k)$.

Step 4. Finding the foci

We have, $(h,k)=(2,1)$.

This implies that, $h=2$and $k=1$.$k=1.$

Further, we have, $c=5$.

Now,

Focilocalid="1647369269234" $$\begin{gathered} =(h,k\pm c) \\ =(2,1\pm 5) \\ =(2,6)or(2,-4) \end{gathered}$$

Therefore, the foci are$(2,6)$and$(2,-4)$