calculus
posted by sze .
Find the point on the line 3 x + 2 y  5 =0 which is closest to the point (4,5).

calculus 
Arora
Take any point on the line as (x,y)
Now, distance between the point on the line and the given point = d
=> d^2 = (x4)^2 + (y5)^2
You can treat this as a function. When d^2 is minimum, then d will be minimum too.
function to minimize = (x4)^2 + (y5)^2
But, y can be written in terms of x:
3x + 2y = 5
=> y = (53x)/2
So, by minimizing the function
f(x) = (x4)^2 + ((3x5)/2)^2
You will get the required point.
Respond to this Question
Similar Questions

Calculus
Find the point on the line 6x + y = 9 that is closest to the point (3,1). Solution: We need to minimize the function d = 
Calculus
Find the point on the line 3x+5y5=0 which is closest to the point (4,0). Please Help! 
CalculusApplied Optimization Problem:
Find the point on the line 6x + 3y3 =0 which is closest to the point (3,1). Note: Your answer should be a point in the xyplane, and as such will be of the form (xcoordinate,ycoordinate) 
Calculus
Find the point on the line 6 x + 4 y  1 =0 which is closest to the point ( 0, 1 ). 
MathCalculus
Find the point on the line 2x + 4y + 3 =0 which is closest to the point (2,1). Note: I have been struggling on this for hours! 
calculus
Find the point on the line 2x+4y+7=0 which is closest to the point (4,−3). 
calculus
Find the point on the line –3x+4y–5=0 which is closest to the point (0–5) 
calculus help amigos
Find the point on the line 5x+5y+7=0 which is closest to the point (3,−4) 
calculus
Find the point on the line 4x+2y+5=0 which is closest to the point (2,1) 
calculus
Ola, I'm not understanding this question, any assistance?