Hi there! I'm back with another problem. I apologize-- my class is getting more difficult and my homework is piling up. It would be a huge favor if someone could help me with this problem:
Let $k$ be a positive real number. The line $x + y = k$ and the circle $x^2 + y^2 = k$ are drawn. Find $k$ so that the line is tangent to the circle.
I think I'm supposed to use desmos? (that is allowed in my course as long as it's helpful to the student).
So, before I submit my answer can someone tell me if the answer: $\boxed{2}$ is right? Thanks so much! I really appreciate it :)
+373 Hey there, Guest!
Yes, you're right, let me show you how:
The distance of the line x+y = k from the centre of the given circle is k/\(\sqrt{2}\)And the circle's radius is \(\sqrt{k}\). Therefore the tangency is (k/\(\sqrt{2}\)) of which equals \(\sqrt{k}\), which is equal to 2.
Hope this helped! :)
( ﾟдﾟ)つ Bye
+373 Hey there, Guest!
Yes, you're right, let me show you how:
The distance of the line x+y = k from the centre of the given circle is k/\(\sqrt{2}\)And the circle's radius is \(\sqrt{k}\). Therefore the tangency is (k/\(\sqrt{2}\)) of which equals \(\sqrt{k}\), which is equal to 2.
Hope this helped! :)
( ﾟдﾟ)つ Bye
