A circle is tangent to the y-axis at y=3 and has one x-intercept at x=1?

Question

(a) Determine the x-intercept
(b) Deduce the equation of the circle.

If possible please explain how you got your answer. Thanks!

Answer 1

>> since the circle is tangent to y-axis, and circle radius is always perpendicular to the tangent, then the circle center must fall on y=3 (a line perp. to y axis at y=3)
this means the center is at (x,3)

>> a general circle equation is (X-x)^2 + (Y-y)^2 = r^2
(r : radius )
y = 3 always.
substitute in this equation with these two points (since they belong to the circle as given)
** X=0 and Y=3
** X=1 and Y=0
you'd get : x = r = 5
and the final equation becomes
(X-5)^2 + (Y-3)^2 = 25

have fune ;)

Answer 2

The center of the circle must be along the y=3.

The x coordinate will be determined by the point where the perpendicualr bisector of the line that goes thru the midpoint of line segment (1,0),(0,3) intersects the line y=3.

This will give you the center and the radius.

Figure out the rest for yourself.