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Question: Answered & Verified by Expert
Point P-1,7 lies on the line 4x+3y=17. Then the coordinates of the points farthest from the line which are at a distance of 10 units from the point P are 
MathematicsStraight LinesJEE Main
Options:
  • A 7,13 and -9,1
  • B 5,15 and -1,-7
  • C -1,5 and 15,-7
  • D 15,5 and -7,-1
Solution:
2018 Upvotes Verified Answer
The correct answer is: 7,13 and -9,1


There are two points A & B which are at a distance of 10 units from P and farthest ( 10 unit distance) from the line 4x+3y=17.

The slope of AB=34 {Because the slope of 4x+3y=17 is -43 }
Let line AB makes an angle θ with x-axis then tanθ=34cosθ,sinθ=45,35
A or B=10cosθ-1,10sinθ+7 or A or B=-10cosθ-1,-10sinθ+7
A or B=7,13 or -9,1

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