Line & Circle?

[Vlatko]

For which value of k the line x = k*y touches the circle
x^2 + y^2 - 10y + 16 = 0 in one point.

[Sam Finch]

The way to do this is to find a polynomial in y for which the line crosses the circle at it's roots, eg

http://161.58.186.97/attachment.php?s=&postid=413425

we now need to find the values of k for which there is only one solution, eg 100-64(k²+1) = 0

solve that and you have your answer.

[Vlatko]

Yes, k is +3/4 or -3/4. I thought so . Thanks.