1. ## inequality question

Find the values of k for which the line y=( 1/2) x + k is a tangent to the curve x^2+y^2=8k

I tried equating the two equations together, making a new combined equation.
from that equation, I took out it's b^2 -4ac and equated it to 0. Haha I hope you can understand what I just wrote.

Anyway If not how should I do this question? Thank you very much!!

2. ## Re: inequality question

Originally Posted by pumbaa213
Find the values of k for which the line y=( 1/2) x + k is a tangent to the curve x^2+y^2=8k

I tried equating the two equations together, making a new combined equation.
from that equation, I took out it's b^2 -4ac and equated it to 0. Haha I hope you can understand what I just wrote.

Anyway If not how should I do this question? Thank you very much!!
Hello,

1. If you solve for x

$x^2+\left(\frac12 x+k\right)^2=8k$

you should come out with

$x = \frac25 \cdot \sqrt{-k} \cdot \left( \sqrt{-k} \pm 2 \sqrt{k-10} \right)$

2. This yields only one value for x if
• $k = 0$: The circle degenerates into a point
• $\sqrt{-k} \pm 2 \sqrt{k-10} = 0$: Solve for k!

3. ## Re: inequality question

Yay got it! thank you sooo much!!