# <span lang="EN-US

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

<span lang="EN-USRS Aggarwal - Mathematics

The distance betwRD Sharma - Mathematics

<span lang="EN-USRS Aggarwal - Mathematics

Find the equationRD Sharma - Mathematics

Find the equationRD Sharma - Mathematics

Area of the trianRD Sharma - Mathematics

<span lang="EN-USRD Sharma - Mathematics

<span lang="EN-USRD Sharma - Mathematics

<span lang="EN-USRD Sharma - Mathematics

A point equidistaRD Sharma - Mathematics