What is the least possible distance between a point on the circle x^2 + y^2 = 1 and a point on the line y = 3/4*x - 3?
A) 1.4
B) sqrt (2)
C) 1.7
D) sqrt (3)
E) 2.0
Wednesday, December 12, 2007
Question # 9
Posted by Gaurav & Kunal at 8:46 PM
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3 Comments:
the equation of the circle shows that the center is (0,0) and radius 1.
Shortest distance from any point on circle will be (shortest distance from origin - radius)
since the shortest distance is perpendicular line form a point, we can represent the equation of that line as y = -4/3x
Solving the two equations, we can find point on the line as (-48/25, 36/25)
Distance from (0,0) to this point is sqrt((48/25)^2 + (36/25)^2) = 2.4
Hence distance from point on the circle is 2.4 -1 = 1.4
Ans: Option A
how the heck would I solve sqrt((48/25)^2 + (36/25)^2) without a calculator???
sivag one more point for you dude.
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