Question 1199583: A circle has its center at (0,0) and its radius is 10 units. Determine the equations of the lines through (15,15) and tangent to the circle.
A. x-2.897y+34.450=0 and x-0.303y-10.450=0
B. x-3.297y+34.450=0 and x-0.303y-10.450=0
C. x-2.897y+34.450=0 and x-0.353y-10.450=0
D. x-23.297y+34.450=0 and x-0.353y-10.450=0
Answer by greenestamps(13200)   (Show Source):
You can put this solution on YOUR website!
ANSWER: B
You won't learn anything from this if we solve the problem for you, so I will outline how you can get the answer and let you do the work.
Let (x,y) be a point on the circle.
The slope of the line from (15,15) to (x,y) is  .
The slope of the radius of the circle from the center (0,0) to (x,y) is  .
A tangent and a radius to the point of tangency are perpendicular, so the product of their slopes is -1:
 [1]
Work with that equation until you get to the point where the equation is  where A is an expression in x and y.
We also know  [2]
so
 [3]
Solve equation [3] for y in terms of x and substitute in [2] to get an equation in x alone.
Use a graphing calculator or similar tool to find the coordinates of the point of tangency.
Note that, by the symmetry of the problem, if one of the points of tangency is (a,-b), then the other point of tangency is (-b,a).
Use the two points of tangency and the fixed point (15,15) to find that the equations of the tangents are as given in answer choice B.
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