Question

Complete the following: Find the intercepts and devast (c) 25r? - 4y - 100 wercises 12.b 16yº 144 (a) 9x (e) **+ y2 = 1 () 9x² + 167 = 144

Answer 1

Given the equation of the hyperbola :

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

Divide both sides by 144

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

So, the last result give us the following :

1. the transverse axis will be parallel to y- axis

2. The center of hyperbola = ( 0 , 0 )

3. There is no points of x- intercepts

4. y- intercepts are : y = -3 , y = 3

So, the points of y- intercepts are ( 0 , -3 ) and ( 0 , 3 )

5. Domain = All real numbers