Question

Hellum ions (alpha particles) are being deflected by gold nucler Figure 127 ad the intercepts and domain and perform the symmetry test on each of the following hyperbolas. te the following: ses 12.6 9x2 - 16y2 = 144 25x2 - 4y2 = 100 -x2 + y2 = 1 _9x2 + 16y2 = 144 (b) 9x² - y² = 9 (d) 25x² - 36y2 = 900 (1) 25x² + 4y = 100 (h) -x + 4y = 16

Answer 1

$\begin{gathered} -x^2+y^2\text{ = 1} \\ y\text{ intercept} \\ \text{make x = 0} \\ y^2\text{ = 1} \\ y\text{ =}\pm\text{ }\sqrt[]{1}\text{ = +1 or -1} \end{gathered}$

At y intercept, the coordinates are (0, 1) (0, -1)

$\begin{gathered} x\text{ inetercepts} \\ \text{make y = 0} \\ -x^2\text{ = 1} \\ x^2=-1 \\ x=\pm\sqrt[]{-1} \\ \text{if }\sqrt[]{-1}=\text{ i} \\ x\text{ = }\pm i \\ x\text{ = +i or -i} \end{gathered}$

At x intercept the coordinates are ( i , 0 ) (-i , 0)

The domain is set of complex numbers

Above is the graph to show you the y intercepts and also to show that it doesnot cut the x axis.