Question

Helium scalpha particles are being cele gode Tecoil Figure 127 xercises 12.6 omplete the following: Find the intercepts and domain and perform the symmetry lest on each of the following byperboles (a) 9x? - 16y2 = 144 (e) + y2 = 1 (g) - 9x + 16y2 = 144 Graph the vertices, foci, endpoints of the conjugate axis, fundamental rectangle, and asymptotes then draw the hyperbola for each equation in problem 1. chord of the partial hyperbola with a (d) 25x - 36 = 900 (1)-25x + 4y = 100 (h) -x + 4y = 16 1. 25x² - 4y2 = 100 (c) 25x2 2.

Answer 1

Given the equation of the hyperbola :

$9x^2-16y^2=144$

Divide all sides by 144

$\begin{gathered} \frac{9x^2}{144}-\frac{16y^2}{144}=1 \\ \\ \frac{x^2}{16}-\frac{y^2}{9}=1 \\ \\ \frac{x^2}{4^2}-\frac{y^2}{3^2}=1 \end{gathered}$

The hyperbola has the following :

1) x - intercepts are = ( -4 , 0 ) and ( 4 , 0 )

2) there is no y- intercepts

3) domain = ( -∞ , -4] ∪ [4 , ∞ )

4) lines of symmetry are : x = 0 and y = 0

$\begin{gathered} a=4,b=3 \\ c^2=a^2+b^2=4^2+3^2=16+9=25 \\ c=\sqrt[]{25}=5 \end{gathered}$

5) foci are the points: (-5 , 0 ) and ( 5 , 0 )