Question

In a hyperbola, if $a=3$ and $c=5$, then $b=$ ________

Short answer

In a hyperbola, of $a=3$and $c=5,$then $b=4$.

Step-by-step solution

Step 1. Given Information

Given that $a=3$and $c=5$.

Aim: We need to find the value of$b$.

Step 2. Concept

For hyperbolas (where $a<c$), the relationship between $a,b$and $c$ is$c^2-a^2=b^2$.

Step 3. Finding the value of b.

We have, $b^2=c^2-a^2$.

Substituting $c=5$and $a=3,$we get,

$$\begin{gathered} b^2=5^2-3^2 \\ {b}^2=25-9 \\ {b}^2=16 \\ b=\sqrt{16} \\ b=4 \end{gathered}$$

Therefore, the value of$b$is$4.$