Chapter 11.5, Problem 12MRE

To determine

To calculate:

  $x-$ Intercept of the hyperbola $4x^2-9y^2=36$ .

Answer to Problem 12MRE

  $x-$ Intercept of the hyperbola $4x^2-9y^2=36$ is $3$ and $-3$ .

Explanation of Solution

Give information:

Expression:

  $4x^2-9y^2=36$

Calculation:

Given is,

  $4x^2-9y^2=36$

To find the $x-$ Intercept, put $y=0$ in equation and solve for $x$ .

Thus,

  $\begin{array}{l}4x^2-9y^2=36\\ 4x^2-9{\left(0\right)}^2=36\\ 4x^2=36\\ x^2=\frac{36}{4}\\ x^2=9\\ x=\pm 3\end{array}$

Therefore, $x-$ Intercept of the hyperbola $4x^2-9y^2=36$ is $3$ and $-3$ .