A circle has center (5,5) and is tangent to the x- and y-axes. If the equation of line l is y=8, what are the x-coordinates of the points of intersection of the line and the circle?
Why is the answer 2.5 and 7.5 and not 4 and 6.
I meant that the answer is 1 and 9!!!
pls help
If your circle has a center at 5,5 and a radius of 5 (it barely touches the axes), this is its equation:
(x - 5)^2 + (y - 5)^2 = 25
When y = 8, solve for x.
@bodangles omg I was putting the radius as 10 - but that wouldn’t make sense.
Why is the radius 5, is that because it is tangent to the axes?
Yup. The center is five blocks away, and if the circle is tangent to both axes, it must just barely brush them there (instead of intersecting in multiple places or not at all). Maybe an easier way to picture it is that the circle and the axes have the same slope at that point. So the bottom of the circle touches the x axis and the left vertical part touches the y.
@bodangles thank you so much, I can’t believe I got caught out by that haha!