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# C2 Coordinate Geometry Circles watch

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1. Im stuck again

A line L has the equation y=mx and a circle C has equation x²+y²-6x-4y+9=0

a) Given that L is a tangent to C find the possible values of m
b) Find the range of values of m given that L intersects C in two distinct points
c) Find the range of the valuse of m given that L and C do not intersect.

2. A line L has the equation y = mx and a circle C has equation x²+y²-6x-4y+9 = 0

a) Given that L is a tangent to C find the possible values of m
a) y = mx, dy/dx = m

So differentiate, x²+y²-6x-4y+9 = 0
re-arrange differential to make dy/dx subject. Let dy/dx = m and solve by letting y = mx in differential.
3. I must be missing something here because none of those questions make any sense. In all of those 3 situations, m could be anything. Have you not been given any coordinates of where it is a tangent to the circle or anything?
4. (Original post by Joe_87)
I must be missing something here because none of those questions make any sense. In all of those 3 situations, m could be anything. Have you not been given any coordinates of where it is a tangent to the circle or anything?
I think by saying the line is y=mx the line must past through the origin?... ...don't know if that helps or not...
5. (Original post by super_baros)
I think by saying the line is y=mx the line must past through the origin?... ...don't know if that helps or not...
Oh yeah, makes sense now, lol. I read things too quickly and obviously just read it as y = mx + c.
6. Rearrange the equation in the form (x-a)²+(y-b)²=r²
to get...
(x-3)²+(y-2)²=4

then if you draw it out.... you that there is a tangent at (1,2) that also crosses the origin.... I think....so just use y2-y1/x2-x1 to find that gradient...

Point 1 - (0,0)
Point 2 - (1,2)
The other value of m is 0 as the circle touches the x axis...

Where the line will intersect at two points will be 0<m<2

And where it won't intersect at all will be m>2 and m<0....

I think it's right.... somebody should check if i'm right...

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Updated: January 26, 2006
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