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Equation of line which is equally inclin...

Equation of line which is equally inclined to the axis and passes through a common points of family of lines `4acx + y(ab + bc + ca- abc) +abc = 0` (where `a, b, c> 0` are in `H.P.)` is

A

`y - x = (7)/(4)`

B

`y - x =- (7)/(4)`

C

`y - x =(1)/(4)`

D

`y -x =- (1)/(4)`

Text Solution

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The correct Answer is:
To find the equation of the line which is equally inclined to the axes and passes through the common point of the family of lines given by \(4acx + y(ab + bc + ca - abc) + abc = 0\), we can follow these steps: ### Step 1: Identify the given family of lines The equation of the family of lines is: \[ 4acx + y(ab + bc + ca - abc) + abc = 0 \] where \(a, b, c > 0\) are in Harmonic Progression (H.P.).
To find the equation of the line which is equally inclined to the axes and passes through the common point of the family of lines given by \(4acx + y(ab + bc + ca - abc) + abc = 0\), we can follow these steps: ### Step 1: Identify the given family of lines The equation of the family of lines is: \[ 4acx + y(ab + bc + ca - abc) + abc = 0 \] where \(a, b, c > 0\) are in Harmonic Progression (H.P.).
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