Graph the hyperbola $y^2 - 9x^2 = 1$ by solving for $y$ and graphing the two equations corresponding to the positive and negative squareroots.
$
\begin{equation}
\begin{aligned}
y ^2 - 9x^2 &= 1 && \text{Model}\\
\\
y^2 &= 1 + 9x^2 && \text{Add } 9x^2 \\
\\
y &= \pm \sqrt{1 + 9x^2} && \text{take the square root}
\end{aligned}
\end{equation}
$
Thus, the hyperbola is described by the graphs of two equations
$y = \sqrt{1+9x^2}$ and $y = -\sqrt{1+9x^2}$
The first equation represents the positive half of the hyperbola because $y \geq 0$ while the second represents the negative half. If we graph the first equation in the viewing recatngle $[-2,2]$ by $[-3,3]$ then we get...
The graph of the second equation is
Graphing these half portions together on the same viewing screen, we get the full hyperbola
Thursday, March 1, 2018
College Algebra, Chapter 2, 2.3, Section 2.3, Problem 30
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