co -od - geo

[nikhilagrawal]

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

[sudhir3127]

My answer is 1.4

The equation of the line will be 3x - 4y - 12 = 0.


This crosses the x and y axis at (0,-3) and (4,0).
the circle has a radius of 1.

So it is closest to the given line when, a perpendicular is drawn to the line, which passes through the origin.This distance of the line from the origin is
12 / sqrt (9 + 16) which is 2.4

Length of perpendicular from origin to line ax +by + c = 0 is mod (c / sqrt (a^2 + b^2)
The radius is 1 unit.


So the shortest distance is 2.4 - 1 unit = 1.4 units

hope its clear

[pepeprepa]

ax +by + c = 0 is mod (c / sqrt (a^2 + b^2)
Could you tell more about this formula? How you find it and other uses?

It depends on the paper you have during the gmat exam (someones knows?) but it is possible to do it with a graph.

[nikhilagrawal]

thats the formula from co od geometery. I would suggest to memorize it. THis formula is applicable for a circle and line concept.