Higher Engineering Mathematics

FUNCTIONS AND THEIR CURVES 193

C

The lengthABis called themajor axisandCDthe
minor axis.
In the above equation, ‘a’ is the semi-major axis
and ‘b’ is the semi-minor axis.
(Note that if b=a, the equation becomes

x^2

a^2

+

y^2

a^2

=1, i.e.x^2 +y^2 =a^2 , which is a circle of

radiusa).

(vii) Hyperbola

The equation of a hyperbola is

x^2

a^2

−

y^2

b^2

= 1

and the general shape is shown in Fig. 19.8. The
curve is seen to be symmetrical about both thex-
andy-axes. The distanceABin Fig. 19.8 is given
by 2a.

AB

O

y

x

x^2 y^2 = 1

a^2 − b^2

Figure 19.8

(viii) Rectangular Hyperbola

The equation of a rectangular hyperbola isxy=cor

y=

c

x

and the general shape is shown in Fig. 19.9.

(ix) Logarithmic Function(see Chapter 4, page 27)

y=lnxandy=lgxare both of the general shape
shown in Fig. 19.10.

(x) Exponential Functions(see Chapter 4, page 31)

y=exis of the general shape shown in Fig. 19.11.

− 3 − 2 − 1 123

− 1

− 2

− 3

1

2

3

0 x

y

y =^ cx

Figure 19.9

01 x

y

y = log x

Figure 19.10

y = ex

(^0) x
1
y
Figure 19.11