write an equation of a circle whos center is at (3,-1) and tangent to the line y=4
what i got so far is this
(x-3)^2 + (y+1)^2 = r^2
what is throwing me off is this tangent of y=4
Since the center is at (3,-1), the tangent line y=4 is the equation of the line that limits how far the point on a circle can be from its center.
So the distance from (3,-1) to (3,4) is what?
It shouldn't be much of a hassle now to get the answer you're looking for.
I hope this helps!
OM is the distance from the center to the tangent.
What Chris used is the fact that the tangent y=4 is horizontal. Thus the line OM is vertical, that is to say any point on this have the same abscissa. Furthermore, M is on the tangent, so its ordinate y is 4.
This is why he asked you to compute the distance from (3, -1) to (3, 4)