SOLUTION:
Case: Hyperbola
Given:
The foci of a hyperbola are at (-6, 3) and (4, 3).
Method:
Because the transverse axis is parallel to the (x or y) -axis, the center will be in the middle of the two foci.
Hence the midpoint about the x-axis is:
[tex]\begin{gathered} x_m=\frac{x_1+x_2}{2},y_m=\frac{y_1+y_2}{2} \\ x_m=\frac{-6+4}{2},y_m=\frac{3+3}{2} \\ x_m=\frac{-2}{2},y_m=\frac{6}{2} \\ x_m=-1,y_m=3 \end{gathered}[/tex]The center of the hyperbola, (h,k) is therefore:
(-1, 3)
Final answer:
(-1, 3)
