P3 circles help. Watch

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Paxi
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#1
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#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
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Freeway
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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
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Aitch
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(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
radius is √(8²+(k/2)²-84)
= √((k²/4)-20) (Do you know all this?)

From equation for C2
radius =6

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
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