FUNCTIONS AND THEIR CURVES 213C
7.x^2 y^2 = 9
[
rectangular hyperbola, lying in
first and third quadrants only]8.x=^13√
(36− 18 y^2 )
⎡⎢
⎣ellipse, centre (0, 0),
major axis 4 units alongx-axis,
minor axis 2√
2 units
alongy-axis⎤⎥
⎦- Sketch the circle given by the equation
x^2 +y^2 − 4 x+ 10 y+ 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 alongy-axis, minor
axis 2 units alongx-axis⎤⎦Graphical solutions to Exercise 85, page 199
Figure 19.39
11.y=√
[3(x^2 −1)]
[
hyperbola, symmetrical aboutx-
andy-axes, vertices 2 units
apart alongx-axis]12.y=√
9 −x^2
[circle, centre (0, 0), radius 3 units]
13.y= 7 x−^1
⎡⎢
⎣rectangular hyperbola, lying
in first and third quadrants,
symmetrical aboutx- and
y-axes⎤⎥
⎦14.y=(3x)^1 /^2 [
parabola, vertex at (0, 0), sym-
metrical about thex-axis]15.y^2 − 8 =− 2 x^2
⎡⎢
⎣ellipse, centre (0, 0), major
axis 2√
8 units along the
y-axis, minor axis 4 units
along thex-axis⎤⎥
⎦