Circles

The question says that
The line with equation y=3x-2 does not intersect the circle with centre (0,0) and radius r. Find the range of possible values of r.

Reply 1

tonyiptony

There should be a worked example that deals with something like this in your textbook somewhere...

That said, two ways:

1, Do you know what does "a line does not intersect a circle" means in terms of equations? Hint, it has something to do with roots of a quadratic (what quadratic? Go have a re-read at your textbook).

2, (Probably not the standard way, but faster) If you happen to know the formula for the distance between a point and a line, the maximum our r can take (well, without actually attaining it) is precisely this distance between the origin and the line. Why? Draw a nice picture and see if you notice something.

(edited 1 year ago)

Reply 2

yzven

Original post by Bird1234

The question says that
The line with equation y=3x-2 does not intersect the circle with centre (0,0) and radius r. Find the range of possible values of r.