Higher Engineering Mathematics

192 GRAPHS

Figure 19.3

Figure 19.4

(v) Circle(see Chapter 14, page 137)

The simplest equation of a circle isx^2 +y^2 =r^2 ,
with centre at the origin and radiusr, as shown in
Fig. 19.5.
More generally, the equation of a circle, centre
(a,b), radiusr, is given by:

(x−a)^2 +(y−b)^2 =r^2

y

r

−r r

−r

x^2 + y^2 = r^2

O x

Figure 19.5

Figure 19.6 shows a circle

(x−2)^2 +(y−3)^2 = 4

024 x

2

3

4

5

y

a = 2

b = 3

r^ =^2

(x−2)^2 +(y−3)^2 = 4

Figure 19.6

(vi) Ellipse

The equation of an ellipse is

x^2

a^2

+

y^2

b^2

= 1

and the general shape is as shown in Fig. 19.7.

AB

C

D

a

b

O x

y

x^2 y^2 = 1

a^2 b^2

+

Figure 19.7