Find all points on the x-axis that are 10 units from the point (7, 6). (Hint: First write the distance formula with (7, 6) as one of the points and (x, 0) as the other point.)

To find all points on the x-axis that are 10 units from the point (7, 6), we can use the distance formula.

The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

In this case, we have the point (7, 6) as one of the points and we need to find the points on the x-axis which have a distance of 10 units from this point. Let's assume that one of those points is (x, 0) where x is the x-coordinate of the point we're looking for.

Substituting the values into the distance formula, we get:
10 = sqrt((x - 7)^2 + (0 - 6)^2)

Simplifying further, we have:
100 = (x - 7)^2 + 36

Now, let's solve for x:

100 = (x - 7)^2 + 36
64 = (x - 7)^2

Taking the square root of both sides, we get:
8 = x - 7 or -8 = x - 7

Solving for x in each equation, we have:
x = 15 or x = -1

So, the two points on the x-axis that are 10 units from the point (7,6) are (15, 0) and (-1, 0).

a circle with radius 10 and center at (7,6)

(x-7)^2 + (y-6)^2 = 10^2 = 100
where does it hit the y axis (y=0) ?

(x-7)^2 + 36 = 100

(x-7)^2 = 64

(x-7) = +/- 8
x = 7 +/- 8

if x = 7+8 then x = 15
if x = 7-8 then x = -1