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The line 3x+y=@ where@is is given meet the x-axis at Aand y axis and B if we will the foot of the perpendicular to AB from the origin over then BC/CA is 9

The line 3x+y=@ where@is is given meet the x-axis at Aand y axis and B if we will the foot of the perpendicular to AB   from the origin over then BC/CA is 9

Grade:11

2 Answers

Arun
25750 Points
5 years ago
 
 I have attached an image in which the solution is given.
Please check and in case of any difficulty please feel free to ask again.
 
 
562-1784_Capture.PNG
 
Now BC /AC = 9/1
Bhagyashri verma
24 Points
5 years ago
Given: Line 1:  x+3y =a 
Line 1 interscets x- axis at A : A=( a/3,0) (put y =0 in eq)
Line 1 intersects y-axis at B: B=(0,a) (put x=0)
Since Line 1 and Line 2 ar perpendicular Hence,
m1m2 = -1 here m1 = slope of line1 = -(1/3) and m2 = slope of line 2 
Therefore, m2 = 3 hence eq of line 2 : x-3y+c =0 
we know line 2 passes through (0,0) hence c =0,
Line 1 and line 2 intersect at C = (3a/10 , a/10)
BC/CA = \sqrt((3a/10)^2 +(a/10-a)^2) /\sqrt((3a/10-a/3)^2 + (a/10)^2) =\sqrt 90 / \sqrt(10/9) = 9
 

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