# Thread: [SOLVED] write an equation for a circle

1. ## [SOLVED] write an equation for a circle

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

2. Originally Posted by john doe
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
The tangent is giving you a hint on the value of the radius.

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!

--Chris

3. I see now but why'd they have to add tangent of y=4 was that just to confuse me?

4. Originally Posted by john doe
I see now but why'd they have to add tangent of y=4 was that just to confuse me?
No, it means that the distance from the center to the tangent equals the radius

See this:

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)