Circle Problem...

A line with slope m is tangent to a circle with its center at the origin. If the line is tangent at (3, 4), what is the value of m? Express your answer as a common fraction.

Spoiler:

This one requires some geometry experience. You have to know that a line tangent to a circle is perpendicular to the line from the point of intersection to the center. So, first, find out the slope of the line from the center to the point of intersection.

(difference in rise)/(difference in run)= 4/3

So, because perpendicular lines have the negative reciprocal (ex. negative reciprocal of 5/6 = -6/5) of each other, the answer is -3/4.

im workin on it ill post my answer as soon as i finish the problem

????ok..... i have no idea... but ill try later

Steve wrote:????ok..... i have no idea... but ill try later

ya that problem is seriously hard

did u come up with this 1??

I agree with Ben's solution to this Geometry problem. For those still working on this problem the following image is a diagram that may be used to reach the solution.

Noting that a perpendicular line has a slope of -1/m, you can carry off from there.



As an additional sidenote, http://www.mathsrevision.net/gcse/pages.php?page=13, discusses in greater detail the concept of a tangent line to a circle and explains how it is perpendicular. The website does contain additional theorem about circles for help in other problems , but a "Ctrl+F" search for tangent will lead you to the information necessary to this problem.