Can someone help me with a circle ?

Question

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

a. what is the other x-intercept

d. deduce to the equation ofa circle

Answer 1

Let's calculate the center of the circle:

It is the same distance from each of the given intercepts,

so the squares of those distances are also equal.

(y - 0)² + (x-1)² = (y - 3)² + x²

y² + x² - 2x + 1 = y² - 6y + 9 + x²

-2x + 1 = -6y + 9

6y - 2x = 8

3y - x = 4

Then center lies on that line.

Since the circle is tangent to the y-axis, that means

the center also lies on the line y = 3

so the x-coordinate of the center is 5  (3*3 - 5 = 4)

Then the equation of the circle is

(x - 5)² + (y - 3)² = 25  (distance from 0,3 to 5,3 squared)

Setting y = 0, we have

x² - 10x + 25 + 9 = 25

x² - 10x + 9 = 0

(x - 1) (x - 9) = 0

and the other x-intercept is at (9,0)

I don't know how to find the other intercept first and then equation of the circle.