What Are the Possible Values of m for a Tangent Line to a Circle?

[Gaz031]

I'm just introducing myself to coordinate geometry in the xy plane of cirlces.
Here's a question I'm having trouble with:

Q11: The line with equation y=mx is a tangent to the circle with equation x^2 + y^2 - 6x - 6y + 17 = 0. Find the possible values of m.

At first i thought i'd try substituting y=mx into the curve equation, but i was still left with 2 unknowns. I don't really know what to do here. Could anyone offer some advice? Thanks.
The answer is (9 (+ or -) root 17) / 8

 

[e(ho0n3]

After substituting you should have

x^2-m^2x^2-6x-6mx+17=0

Rearrange this and you get

(1+m^2)x^2 - (6m+6)x + 17 = 0

Let a = 1 + m², b = -(6m + 6) and c = 17. Then use the quadratic equation (and remember that you want the expression under the square root to be greater than or equal to 0).

 

[Gaz031]

Your latex looks ok. Do you mean rearrange to form:
x^2 ( 1+ m^2) - x(6m+1) + 17 = 0 ?

Edit: Ah yes you typed that below. I'll try that now.

 

[e(ho0n3]

I re-edited my post. Please have a look.

 

[Gaz031]

I get it. So you say that b^2 - 4ac = 0. Then form yet another quadratic equation, tidy up and simplify. I haven't had much experience of using brackets as coefficients in the quadratic equation but that's something I'm going to remember for the future.

Thanks for the help!

 

[e(ho0n3]

That should be b² - 4ac ≥ 0.