Q. 135.0( 3 Votes )

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Answer :

Given: (x1,y1) = A ( – 2, – 7)

To find:


Equation of required line.


Explanation:



So, the equation of the line is


Formula Used:



Let the required line intersect the lines 4x + 3y = 3 and 4x + 3y = 12 at P1 and P2.


Let AP1 = r1 and AP2 = r2


Then, the coordinates of P1 and P2 are given by and respectively. Thus, the coordinates of P1 and P2 are ( – 2 + r1cos θ, – 7 + r1sin θ) and ( – 2 + r2cos θ, – 7 + r2sin θ), respectively.


Clearly, the points P1 and P2 lie on the lines 4x + 3y = 3 and 4x + 3y = 12


4( – 2 + r1cos θ) + 3( – 7 + r1sin θ) = 3 and 4( – 2 + r2cos θ) + 3( – 7 + r2sin θ) = 12,


and


Here AP2 – AP1 = 3




3 = 4 cos θ + 3 sin θ


3(1 – sin θ) = 4cos θ


9(1 + sin2 θ – 2sin θ) = 16 cos2 θ = 16(1 – sin2 θ)


25 sin2 θ – 18 sin θ – 7 = 0


(sin θ – 1)(25 sin θ + 7 ) = 0


Sin θ = 1, sin θ = – 7/25


Cos θ = 0, cos θ = 24/25


Thus, the equation of the required line is


x + 2 = 0 or


x + 2 = 0 or 7x + 24 y + 182 = 0


Hence, the equation of line is x + 2 = 0 or 7x + 24 y + 182 = 0


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