Chris Cross wrote:Hello,
Please help me understand how to solve the following problem quickly:
What is the least possible distance between a point on the circle x² + y² = 1 and a point on the line y = (3/4)x - 3?
x^2+y^2=1; represents circle having center (0,0) and radius=1,
now the line y=(3/4)x-3; intersects the x and y axis at the point (4,0) and (0,-3) respectively,if we plot the graph of the line and circle we will notice that least distance between the line and the point on the circle = (distance b/w the origin and line)-radius..!! (plot the graph you'll notice why i subtracted r from the distance b/w the origin and line.);
distance between the point (m,n) and line ax+by+c=0 can be found by using the distance formula..!!!
d=|am+bn+c|/sqrt(a^2+b^2)......1);
here (m,n)=(0,0)
a=-3/4,
b=1,
c=-3,
substituting above values in 1) we have;
|-3|/sqrt(9/16+1);
3/(5/4)=12/5;
hence required minimum distance=12/5-1;
7/5=1.4..!!!
i hope it helps...!!!
O Excellence... my search for you is on... you can be far.. but not beyond my reach!
