SOLUTION: center: (2,15) point on circle: (5,15) write the equation of each circle with the given information. then write the equation of the line tangent to the circle at the given point.

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: center: (2,15) point on circle: (5,15) write the equation of each circle with the given information. then write the equation of the line tangent to the circle at the given point.      Log On


   

Question 877742: center: (2,15)
point on circle: (5,15)
write the equation of each circle with the given information. then write the equation of the line tangent to the circle at the given point. (Hint: You will need both length and slope of the radius.)
Found 2 solutions by Fombitz, richwmiller:
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Find the radius by using the distance between the center and the point.
R%5E2=%282-5%29%5E2%2B%2815-15%29%5E2
R%5E2=%28-3%29%5E2
R=3
.
.
%28x-2%29%5E2%2B%28y-15%29%5E2=9
Take the derivative to find the slope of the tangent line at any point,
2%28x-2%29%2B2%28y-15%29=0
%282x-4%29dx%2B%282y-30%29dy=0
%282y-30%29dy=%284-2x%29dx
dy%2Fdx=%284-2x%29%2F%282y-30%29
m=dy%2Fdx=%282-x%29%2F%28y-15%29
At x=5,
m=%282-5%29%2F%2815-15%29
The slope is infinite at that point.
x=5 is the tangent.

Answer by richwmiller(17219) About Me  (Show Source):
You can put this solution on YOUR website!
There is no such thing as an infinite slope.
This slope is undefined.