Solution
- The equation of a hyperbola is given s:
[tex]\begin{gathered} \frac{(x-h)^2}{a}-\frac{(y-k)^2}{b}=1 \\ \\ where, \\ coordinates\text{ of the vertices}=(h\pm a,k) \\ Length\text{ of conjugate axis}=2b \end{gathered}[/tex]- Thus, we can find that:
[tex]\begin{gathered} (\pm2,0)=(h\pm a,k) \\ \\ k=0 \\ \therefore h+a=2 \\ h-a=-2 \\ \text{ Subtract both equations, we have:} \\ 2a=4 \\ a=\frac{4}{2}=2 \\ \\ h+a=2 \\ h+2=2 \\ h=2-2=0 \\ \\ \text{ Thus, we have that the center of the hyperbola is: }(h,k)=(0,0) \\ \\ 2b=14 \\ \text{ Divide both sides by 2} \\ b=\frac{14}{2}=7 \end{gathered}[/tex]Final Answer
The equation of the parabola is:
[tex]\frac{x^2}{2^2}-\frac{y^2}{7^2}=1[/tex]