SOLUTION: Find a general form of an equation of the line that is tangent to the circle at the point P. x 2 + y 2 = 100; P ( 8, 6 )

Algebra ->  Circles -> SOLUTION: Find a general form of an equation of the line that is tangent to the circle at the point P. x 2 + y 2 = 100; P ( 8, 6 )      Log On


   

Question 270996: Find a general form of an equation of the line that is tangent to the circle at the point P.
x 2 + y 2 = 100; P ( 8, 6 )
Answer by drk(1908) About Me  (Show Source):
You can put this solution on YOUR website!
We have a circle with radius 10 centered at (0,0) and passing through (8,6).
The slope of (0,0) and (8,6) is
m+=+3%2F4
but we want the perpendicular slope for the tangent line as
+m+=+_4%2F3
---
The equation is expressed as
y+=+mx+%2B+b
and putting in our slope, -4/3 and point, (8,6) we get
6+=+%28-4%2F3%29%2A8+%2B+b
which is
6+=+-32%2F3+%2B+b
and then
b+=+50%2F3
The answer is
y+=+%28-4%2F3%29x+%2B+50%2F3