Question

8. What is the equation of a hyperbola with a = 6 and c = 87 Assume that the transverse axis is horizontal.x2 y?- 136 28164 36--- 128 36

Answer 1

The equation of a hyperbola when the transverse axis is horizontal is given as

`\begin{gathered} (x^2)/(a^2)-(y^2)/(b^2)=1 \\ \text{where c}^2=a^2+b^2 \end{gathered}`

Given that a=6, c=8, let us solve for b using

`\begin{gathered} c^2=a^2+b^2 \\ b^2=c^2-a^2 \\ b^2=8^2-6^2^{} \\ b^2=64-36 \\ b^2=28 \end{gathered}`

Note that b²=28 and a²=6²=36

Substituting into the equation will give

`\begin{gathered} (x^2)/(a^2)-(y^2)/(b^2)=1 \\ (x^2)/(36)-(y^2)/(28)=1 \end{gathered}`

Hence, the correct answer is the first option