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  • Given the family of lines, <img alt="a (3x + 4y + 6) + b (x + y + 2) = 0" src="https://entrancecorner.oncodecogs.com/gif.latex?a%20%283x%20&plus;%204y%20&plus;%206%29%20&plus;%20b%

Given the family of lines, a (3x + 4y + 6) + b (x + y + 2) = 0 . The line of the family situated at the greatest distance from the point P (2, 3) has equation

Option: 1

4x + 3y + 8 = 0


Option: 2

5x + 3y + 10 = 0


Option: 3

15x + 8y + 30 = 0


Option: 4

none


Answers (1)

best_answer

 

Two – point form of a straight line -

y-y_{1}=\left ( \frac{y_{2}-y_{1}}{x_{2}-x_{1}} \right )(x-x_{1})

 

- wherein

The lines passes through  (x_{1}y_{1})  and  (x_{2}\, y_{2})

 

 

Equation of a line perpendicular to a given line -

Bx-Ay+\lambda =0  is the line perpendicular to Ax+By+C =0 .

 

- wherein

  \lambda is some other constant  than C.

 

 

point of intersection is A (- 2, 0) . The required line will be one which passes through (- 2, 0) and is perpendicular to the line joining A(- 2, 0) and B(2, 3) 

slope of AB = 3/4

Hence, slope of required line will be -4/3

Hence, required line will be 4x + 3y + k = 0 which passes through (-2, 0).

Hence, required line is 4x+3y+8 = 0 .

Posted by

avinash.dongre

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