# How do you graph x^2/14^2 - y^2/11^2 =1?

Nov 5, 2015

See explanation
The final plot instruction and calculation method given.

#### Explanation:

I will not bother to square the 14 and 11 for simplicity on my side!

${y}^{2} / {11}^{2} = {x}^{2} / {14}^{2} - 1$

${y}^{2} = \frac{{11}^{2} x}{14} ^ 2 - {11}^{2}$

so
$y = \sqrt{\frac{{11}^{2} x}{14} ^ 2 - {11}^{2}}$

~~~~~~~~~~~~ Side Note ~~~~~~~~~~~~~~~~~~~~

Suppose $\sqrt{\frac{{11}^{2} x}{14} ^ 2 - {11}^{2}} = b$

then $\left(- b\right) \times \left(- b\right) = \left(+ b\right) \times \left(+ b\right) = y$
So the square root can be both positive or negative.

~~~~~~~~~~~ Back to the problem ~~~~~~~~~~~~~~~~~~~~~~~~~

To obtain the plotting values of y

$y = \pm \sqrt{\frac{{11}^{2} x}{14} ^ 2 - {11}^{2}}$

Just insert your values for x and plot both the positive and negative values of $y$ against that value of $x$