What are the exact values of k for which the line y=kx+3 is tangent to the circle with centre (6,3) and radius 2?


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Question Number 124928 by bemath last updated on 07/Dec/20

$W h a t a r e t h e e x a c t v a l u e s o f k$ $f o r w h i c h t h e l i n e y = k x + 3$ $i s t a n g e n t t o t h e c i r c l e w i t h$ $c e n t r e (6, 3) a n d r a d i u s 2 ?$
	Answered by mr W last updated on 07/Dec/20

	$2 = \frac{6 k - 3 + 3}{\sqrt{k^{2} + 1}}$ $8 k^{2} = 1$ $\Rightarrow k = \pm \frac{\sqrt{2}}{4}$
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