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

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Evaluate multi-variable expressions

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Q. In a hyperbola if

a = 3

and

c = 5

then

b =

______

Understand relationship in hyperbola: Understand the relationship between $a$ , $b$ , and $c$ in a hyperbola. $\newline$ The relationship between $a$ , $b$ , and $c$ in a hyperbola is given by the equation $c^2 = a^2 + b^2$ , where $c$ is the distance from the center to a focus, $a$ is the distance from the center to a vertex, and $b$ is the distance from the center to the co-vertex.
Substitute values into equation: Substitute the given values of $a$ and $c$ into the hyperbola equation. $\newline$ Substitute $a = 3$ and $c = 5$ into the equation $c^2 = a^2 + b^2$ to find $b$ . $\newline$ $5^2 = 3^2 + b^2$
Calculate $b^2$ : Calculate $b^2$ . $\newline$ $25 = 9 + b^2$ $\newline$ $b^2 = 25 - 9$ $\newline$ $b^2 = 16$
Solve for b: Solve for b. $\newline$ Since $b^2 = 16$ , take the square root of both sides to find $b$ . $\newline$ $b = \sqrt{16}$ $\newline$ $b = 4$

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