# P3 circles help.Watch

This discussion is closed.
Thread starter 13 years ago
#1
I've attached the figure ... i have also got the marking shceme of this paper but that doesn't explain the steps ... so i'll be grateful if anyone can solve the following question and explain each step :-)

Fig. 1
Figure 1 shows the circles C1 and C2. Circle C1 has the equation

x2 + y2 − 16x − ky + 84 = 0,
where k is a positive constant.

(a) Find in terms of k
(i) the coordinates of the centre of C1,
(ii) the radius of C1. (5 marks)

Circle C2 has the equation
x2 + y2 – 36 = 0.
Given that circles C1 and C2 are touching,
(b) find the value of k.

http://img.photobucket.com/albums/v6...gm/circles.jpg
0
13 years ago
#2
not too sure about b)

but i think a) is:

equation: x^2 + y^2 - 16x - ky + 84 = 0
(x-8)^2 + (y-0.5k)^2 = -84+64+(0.5k)^2

therefore centre is (8,0.5k) and radius^2=-20+0.5k^2
0
13 years ago
#3
(Original post by Paxi)
I've attached the figure ... i have also got the marking shceme of this paper but that doesn't explain the steps ... so i'll be grateful if anyone can solve the following question and explain each step :-)

Fig. 1
Figure 1 shows the circles C1 and C2. Circle C1 has the equation

x2 + y2 − 16x − ky + 84 = 0,
where k is a positive constant.

(a) Find in terms of k
(i) the coordinates of the centre of C1,
(ii) the radius of C1. (5 marks)

Circle C2 has the equation
x2 + y2 – 36 = 0.
Given that circles C1 and C2 are touching,
(b) find the value of k.

http://img.photobucket.com/albums/v6...gm/circles.jpg

From equation for C1
centre is (8,k/2) and
= √((k²/4)-20) (Do you know all this?)

From equation for C2

So (distance between origin and centre of C1)² = (6+√((k²/4)-20) )²

By Pythag. this = 8² + (k/2)²

Solve (6+√((k²/4)-20) )² = 8² + (k/2)²
Get k = 12

This gives C1 centre at (8,6) and C1 radius as 4, which all looks OK.

Aitch
0
X
new posts
Latest
My Feed

### Oops, nobody has postedin the last few hours.

Why not re-start the conversation?

see more

### See more of what you like onThe Student Room

You can personalise what you see on TSR. Tell us a little about yourself to get started.

### University open days

• University of Derby
Postgraduate and Professional Open Evening - Derby Campus Postgraduate
Tue, 22 Jan '19
• University of the West of England, Bristol
Undergraduate Open Afternoon - Frenchay Campus Undergraduate
Wed, 23 Jan '19
• University of East London
Wed, 23 Jan '19

### Poll

Join the discussion

Remain (1581)
79.29%
Leave (413)
20.71%