7. The equation of a curve is xy=10 and the equation of a line l is 2x+y=q, where q is a number.
(i) Find the set of values of q for which l does not intersect the curve.
I am on the right track I think but I don't know how to get the answer. I will upload a picture of my working out but basically I got q

Question

7. The equation of a curve is xy=10 and the equation of a line l is 2x+y=q, where q is a number.
(i) Find the set of values of q for which l does not intersect the curve.
I am on the right track I think but I don't know how to get the answer. I will upload a picture of my working out but basically I got q<square root of 80 (which I incorrectly worked out to be 8.9 and used that but anyway).

anonymous · Answer

and the actual answer is $$-\sqrt{80}<q<\sqrt{80}$$

anonymous · Answer

So basically I don't know why this is the answer or how to get it. Please help!

anonymous · Answer

attachment

anonymous · Answer

The coordinates that I marked are from a previous question. But thats my working out

zpupster · Answer

yes that is correct https://www.desmos.com/calculator/m3ynz8wrtz

anonymous · Answer

So are you saying that their answer is just a different form of mine?