Question

awr of p(x)?.
31. An exhibition is being organised in the school premises to highlight "Swatchebih
Bharat Abhiyan' and 'Say no to plastic'. Material concerning these is displayed at
the positions represented by the points A(-4,0) and B(4,0). A spot light is placed
at a point represented by P(a, b) such that A, B and P are equidistant from each
other.
(i) Help me in finding the position of point P by finding the values of a and b.
(ii) The distance of point P from line segment AB.​

Answer 1

P = ( 0 , ± 4√3) , 4√3 is Distance of point P from line  segment AB

Step-by-step explanation:

A  ( - 4, 0)

B  ( 4, 0)

P ( a , b)

PA = PB  = AB

AB = √(4 -(-4))² + (0 - 0)²  = 8

PA = PB  =   √(a + 4)² + b²  = √(a - 4)² + b²

(a + 4)² + b² = (a - 4)² + b²

=>  a² + 16 + 8a = a² + 16 - 8a

=> 16a = 0

=> a = 0

PA = PB  =   √4² + b²

√4² + b² = 8

=> 16 + b² = 64

=> b² = 48

=> b = ± 4√3

P = ( 0 , ± 4√3)

4√3 is Distance of point P from line  segment AB

AB Slope = 0  => AB Parallel to x axis

PM ⊥ AB   =>  PM ⇒ y axis

P ( 0 , ± 4√3)  => M = ( 0 , 0)

4√3 is Distance of point P from line  segment AB

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