Posted by **alk** on Sunday, August 3, 2008 at 11:30am.

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

a) Determine the other x-intercept.

b) Find the equation of the circle.

Thanks for helping!

- math -
**Damon**, Sunday, August 3, 2008 at 3:48pm
Well, if it is tangent to the y axis at (0,3), then the center must be somewhere on the horizontal line y = 3 because the radius is perpendicular to the tangent.

So if center is at (a,3)

(x-a)^2 + (y-3)^2 = r^2

we know when x = 0, y = 3 so

a^2 = r^2

so

(x-a)^2 + (y-3)^2 = a^2

now when y = 0, x = 1 and something else

(1-a)^2 +9 = a^2

1 -2a +a^2 +9 = a^2

a = 5 = r

so center is at (5,3)

(x-5)^2 + (y-3)^2 = 25

is the equation

x intercepts:

(x-5)^2 +9 = 25

x^2 - 10 x + 25 + 9 = 25

x^2 -10 x = -9

x^2 - 10 x + 25 = 16

(x-5)^2 = 16

x-5 = +/- 4

x = 1 or x = 9

which you could have seen from a sketch once you knew the radius was 5 and the center at (5,3)

## Answer This Question

## Related Questions

- calc - a circle is tangent to the y-axis at y=3 and has one x-intercept at x=1 1...
- math - a circle is tangent to the y-axis at y=3 and has one x-intercept at x=1 a...
- Math - A circle is tangent to the y-axis at y=3 and has one x-intercept at x=1, ...
- math - 1. two circles. x^2+y^2-16x-8y+35=0 and x^2+y^2=5 are given. a. write the...
- mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....
- mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....
- mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....
- maths - 1) Circle centre (7,-2) passes through (-2,10). Calculate radius and ...
- mathematics - The circle x2-2x+y2-4y-4=0 lies on the cartesian plane,question 2....
- Math - Find the equation of the circle that passes through the origin and x-...

More Related Questions