number of straight lines which are at a unit distance from each of the points P(1,2) and Q(8,5) are
Answers
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Given : number of straight lines which are at a unit distance from each of the points P(1,2) and Q(8,5)
To find : Number of lines
Solution:
let say Equation of lines at unit Distance from P & Q
Ax + By + C = 0
Distance of point from line
d = |Ax₁ + By₁ + C | /√(A² + B²)
P(1,2)
=> 1 = | A + 2B + C | /√(A² + B²)
=> √(A² + B² ) = | A + 2B + C |
Q(8,5)
=> 1 = | 8A + 5B + C | /√(A² + B²)
=> √(A² + B² ) = | 8A + 5B + C |
Case 1 :
A + 2B + C = 8A + 5B + C
=> 7A = - 3B
These will give two lines
Case 2 :
A + 2B + C = -(8A + 5B + C)
=> 9A = 3B - 2C
These will lead to infinite lines
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