SOLUTION: for what value(s) of m is the line y = mx + 5 at a distance 4 from the origin?

Question 970828: for what value(s) of m is the line y = mx + 5 at a distance 4 from the origin?
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
for what value(s) of m is the line y = mx + 5 at a distance 4 from the origin?
-----------------------
All points on a circle about the Origin with r = 4 are 4 units from the Origin.
Find the intersections of
y = mx + 5 and

----

------------------
That doesn't look promising.
Try this:
The slope at any point on the circle is -x/y.
---
y = mx + 5
m = (y-5)/x = -x/y
x^2 = -y^2 + 5y --> x^2 + y^2 = 5y
5y = 16
y = 3.2
---
x^2 + y^2 = 16
x^2 = 16 - 3.2^2 = 5.76
x = -2.4, +2.4
------------
The 2 tangent points are (-2.4,3.2) and (2.4,3.2)
The y-int of y = mx + 5 is (0,5)
1 slope = (5-3.2)/2.4 = +0.75
The other is -0.75

RELATED QUESTIONS
For what value(s) of m is the line y = mx + b at a distance 3 from (4,1)... (answered by Theo)

Find an equation(s) of the line(s) containing (5, 1) and at a distance 1 from the... (answered by Alan3354)

Please help with the homework: The graph of the function F, which is a straight line... (answered by ikleyn)

A point moves in a straight line so that its distance s from the origin at time t is... (answered by Alan3354)

a tiger is at the origin of coordinates at time t1=0 secs. For the time interval from... (answered by macston)

For what values of m is the line y= mx a tangent to the parabola y=x^2 - 8x +... (answered by ikleyn)

the equation of a line y=mx-1. what is the value of m if the line passes through the... (answered by Alan3354)

Please help me find the exact value of the shortest distance from the origin to each... (answered by scott8148)

The line L passes through the point (-1,1) and is perpendicular to a line with a slope of (answered by stanbon)