Higher Engineering Mathematics, Sixth Edition

200 Higher Engineering Mathematics

8. x=^13

√

( 36 − 18 y^2 )

⎡

⎢

⎢

⎣

ellipse,centre( 0 , 0 ),

major axis 4 units alongx-axis,

minor axis 2

√

2 units

alongy-axis

⎤

⎥

⎥

⎦

9. 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

⎤

⎦

11. y=

√

[3(x^2 − 1 )]

Graphical solutions to Exercise 77, page 186

y 53 x 25

y 5 x^213

y 523 x 14

123

10

5

(^0) x
y
25
22 21 1 2
8
6
4
2
(^0) x
y
123
4
2
(^0) x
y
22
y 5 (x 2 3)^2
246
8
4
(^0) x
y

1. 
   

3. 
   
   
   
   4. 
      
   
   
   
   

2.

Figure 18.39

⎡

⎣

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=( 3 x)^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

⎤

⎥

⎥

⎦