Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P,is

Slope of a line passing through P(2, 3) and intersecting the line, x + y = 7 at a distance of 4 units from P,

is

  1. A

    151+5

  2. B

    717+1

  3. C

    515+1

  4. D

    171+7

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    Solution:

    Let x=2+rcosθ and 

    y=3+ r sin θ be points of

    intersection.

    Now, x+y=7                                 [Given] 

    2+rcosθ+3+rsinθ=7r(sinθ+cosθ)=2sinθ+cosθ=2r=2±4=±12(sinθ+cosθ)2=14

    1+sin2θ=14sin2θ=342tanθ1+tan2θ=34

    2m1+m2=34, where m is slope of required line 

    3m2+8m+3=0m=8±64366=4±73

     Consider,171+7=171+7×1717=(17)217

    =1+7276=8276=4+73

    Thus, option (d) satisfies the above condition.

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