CracktheGmat2010 wrote:

What is the least possible distance between a point on the circle \(x^2 + y^2 = 1\) and a point on the line \(y = \frac{3}{4}x - 3\) ?

\(1.4\)

\(\sqrt{2}\)

\(1.7\)

\(\sqrt{3}\)

\(2.0\)

Can anyone Please explain this Question??

The question has been discussed before. This is my take on it.

Look at the diagram below and forget the circle for the time being. What is the minimum distance from the center (0,0) to the line? It will the perpendicular from the center to the line, right? (shown by the bold line)

Attachment:

File.jpg

Now think, what will be the shortest distance from the circle to the line? It will be 1 unit less than the distance from the center to the line. Can we say it will be the least in case of the bold line which is perpendicular to the given line? Yes, it will be because in all other cases, the lines are longer than the perpendicular and hence (line - 1) will also be longer.

Then, let's try to find the length of the bold line, x.

Since hypotenuse is 5,

(1/2)*3*4 = (1/2)*5*x = Area of triangle made by the co-ordinate axis and the given line

x = 2.4

So minimum distance is 2.4 - 1 = 1.4

tell me where i am going wrong.