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-

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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