SOLUTION: Show that the tangents to the circle x^2+y^2=100 at the points (6,8) and (8,-6) are perpendicular to each other.

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Question 687468: Show that the tangents to the circle x^2+y^2=100 at the points (6,8) and (8,-6) are perpendicular to each other.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!


Draw the radius to (6,8). We use the slope
formula to find its slope.  It passes through
(x1, y1) = (0,0) and (x2, y2) = (6,8).  

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m = %288-0%29%2F%286-0%29 = 8%2F6 = 4%2F3 = slope of radius to (6,8)

The red line is perpendicular to the radius drawn to to (6,8) because a 
tangent is perpendicular to a radius drawn to the point of tangency.
Therefore the slope of the red line is the negative reciprocal of the 
slope of the radius to (6,8).  So the red line's slope is -3%2F4.

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Draw the radius to (8,-6). 




We use the slope
formula to find its slope.  It passes through
(x1, y1) = (0,0) and (x2, y2) = (8,-6). 

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

m = %28-6-0%29%2F%288-0%29 = -6%2F8 = -3%2F4

The green line is perpendicular to the radius drawn to to (8,-6) because a 
tangent is perpendicular to a radius drawn to the point of tangency.
Therefore the slope of the green line is the negative reciprocal of the 
slope of the radius to (8,-6).  So the green line's slope is 4%2F3.

The red line is perpendicular to the green line because the red
line's slope is -4%2F3 and the green line's slope is 3%2F4
and they are negative reciprocals.

Edwin