posted by Anonymous .
a circle is tangent to the y-axis at y=3 and has one x-intercept at x=1
a) what's the other x-intercept
b) what's the equation
i have no clue how to solve this!
You know that the center of the circle is somewhere in the line y = 3, denote the x-coordinate by rx. Then the radius of the circle is |rx|. The distance from the center to the point x = 1 on the x-axis must be equal to the radius, which is |rx|. Therefore:
(rx-1)^2 + 9 = rx^2 --->
rx = 5.
Equation of the circle is thus:
(x - 5)^2 + (y - 3)^2 = 25
And you see that the other x intercept is at x = 9