EXERCISE 4.4
Sketch the graph of each of the following.
1. \( \frac{(x-1)^{2}}{25}+\frac{(y+2)^{2}}{16}=1 \)
3. \( \frac{x^{2}}{100}+\frac{(y-1)^{2}}{25}=1 \)
2. \( \frac{(x+3)^{2}}{36}+\frac{(y-4)^{2}}{45}=1 \).
4. \( 18(x-2)^{2}+24 y^{2}=432 \)
Find the equation of the ellipse satisfying the given condition and sketch the graph.
5. Vertices at \( (4,2) \) and \( (12,2) \), length of semiminor axis 3
6. Foci at \( (1,3) \) and \( (7,3) \), length of major axis 10
7. Center at \( (3,5) \), a vertex at \( (-2,5) \), a focus at \( (6,5) \)
8 A vertex at \( (8,0) \), end of minor axis at \( (4,3) \), major axis horizontal.
9. A focus at \( (-3,-1) \), one end of minor axis at \( (0,3) \), major vertical
10. Foci at \( (-4,0) \) and \( (-4,6) \), a vertex at \( (-4,8 \);
11. Center at \( (2,3) \), a vertex at \( (2,-1) \), iaius rectum \( 9 / 2 \)
Using Fig. 4.23,
12. Derive equation \( E \) (4.14)
13. Show that the length of the latus rectum is \( 2 b^{2} / a \).
