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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

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