Posted by **Emily** on Wednesday, April 30, 2008 at 7:09pm.

Line l is tangent to circle O at point P(3,4) where the center is located at (0,0).

a. Find the radius of the circle. (I got 4)

b. Give an equation of the circle. (I got x^2+y^2=16)

c. Find the slope of line l.

d. Give an equation of line l.

---------------------------------------------------------------------------------------------------

I can't figure out what the slope would be, if I knew that I could figure out (d). Does anybody know how to do this?

- Math (geometry) -
**JP**, Friday, May 9, 2008 at 12:56am
Since the line is tangent at a point to the circle, then the point lies on the circle. Also, since you know the center, the radius is simply the distance between the points (0,0) and (3,4).

a) So, radius=d=sqrt((3-0)^2+(4-0)^2)=5

b) x^2+y^2=25

c) Observe that the radius is perpendicular to the tangent line. Thus, if you can find the slope using the coordinates of endpoints of the radius (i.e. (0,0) and (3,4)) then the negative reciprocal of this value will give the slope of the tangent line. Answer is -3/4.

d) Since you know the slope (-3/4) and the point (3,4) is on the line, we can use the form y=mx+b. If you go through the motions, you'll find that y=(-3/4)x+(25/4)

## Answer this Question

## Related Questions

- calc - standard equation of circle concentric with X^2+Y^2-2X-8Y+1=0 and tangent...
- GEOMETRY INSCRIBED ANGLES MULTIPLE CHOICE QUESTION - segment BC is tangent to ...
- GEOMETRY CIRCLE - 1.An isosceles triangle with each leg measuring 13 cm is ...
- GEOMETRY CIRCLES PLEASE - 1.An isosceles triangle with each leg measuring 13 cm ...
- Math (Pre Cal) - Hi, I am studying for a precalculus quiz and I do not ...
- Math - I have a series of questions that I did. They lead up to the last ...
- math - a circle is tangent to the y-axis at y=3 and has one x-intercept at x=1 a...
- Geometry - Within an orthonormal system consider points A(1,4) B(5,1) C(4,8) (a)...
- GEOMETRY CIRCLES PLEASE - HELP ME PLEASE. 1.An isosceles triangle with each leg...
- Geometry - I have a circle with a Tangent line, DE, running along it and ...