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Helium Gris Talpha particles are being delleced by contest being detected Figure 127 ripere the following: Find the intercepts and domain and perform the symmetry test on each of the following hyperbolas. (aa) 9 - 16 - 144 (c) 254" - 40? Graph the vertices, foci, endpoints of the conjugate axis, fundamental rectangle, and asymptotes, then draw the hyperbola for each equation in problem 1.. 100 36y2 = 900 16y2 = 144 = 100 of the partial hou. (b) 9x - y 25x? (1) -25x2 + (h) x2 + 4y = 16 (g) -92

Answer :

This is the hyperbola, a=1, b=3

Vertices are (-1,0) and (1,0)

Intercepts are (-1,0) and (1,0)

Domain is all real numbers from -ve infinity to +ve infinity

Lines of symmetry are the lines x=0 , y=0

[tex]\begin{gathered} c=\text{ }\sqrt[]{a^2+b^2}=\sqrt[]{1+9}=\sqrt[]{10} \\ \text{Focus =(-}\sqrt[]{10},\text{ 0) and (}\sqrt[]{10},\text{ 0)} \end{gathered}[/tex]

For the asymptyotes

[tex]\begin{gathered} y=\pm\frac{b}{a}x\text{ } \\ y=\pm3x \end{gathered}[/tex]

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