200 Higher Engineering Mathematics
8. x =
1
3
(36 − 18y 2 )
⎡
⎢
⎢
⎣
ellipse, centre (0, 0),
major axis 4 units along x-axis,
minor axis 2
√
2 units
along y-axis
⎤
⎥
⎥
⎦
9. Sketch the circle given by the equation
x 2 + y 2 − 4x + 10y + 25 =0.
[Centre at (2, −5), radius 2]
In Problems 10 to 15 describe the shape of the
curves represented by the equations given.
10. y =
[3(1 − x 2 )]
⎡
⎣
ellipse, centre (0, 0), major axis
2
√
3 units along y-axis, minor
axis 2 units along x-axis
⎤
⎦
11. y =
[3(x 2 − 1)]
Graphical solutions to Exercise 77, page 186
y 5 3x 25
y 5 x
2 13
y 5 23x 14
1
2
3
10
5
0
x
y
25
21
22
1
2
8
6
4
2
0
x
y
1
2
3
4
2
0
x
y
22
y 5(x 23) 2
2
4
6
8
4
0
x
y
1.
3.
4.
2.
Figure 18.39
⎡
⎣
hyperbola, symmetrical about xand y-axes, vertices 2 units
apart along x-axis
⎤
⎦
12. y =
√
9 − x 2
[circle, centre (0, 0), radius 3 units]
13. y = 7x −1 ⎡
⎢
⎢
⎣
rectangular hyperbola, lying
in first and third quadrants,
symmetrical about x- and
y-axes
⎤
⎥
⎥
⎦
14. y = (3x) 1/2
parabola, vertex at (0, 0), symmetrical about the x-axis
15. y 2 − 8 =−2x 2
⎡
⎢
⎢
⎣
ellipse, centre (0, 0), major
axis 2
√
8 units along the
y-axis, minor axis 4 units
along the x-axis
⎤
⎥
⎥
⎦