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

linex = 2.4

So minimum

distance is 2.4 - 1 = 1.4

tell me where i am going wrong.