There are 2 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&P are equidistant from each other.
(i) Find positⁿ of point P by finding the values of a and b.
(ii)The distance of point P from line segment AB.
(i) Find positⁿ of point P by finding the values of a and b.
(ii)The distance of point P from line segment AB.
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I) The position of point P is either (0,-√48) or (0,√48).
II) The distance of P from line segment AB is √42 units.
The point P is placed such that A,B and P are equidistant to each other.
AB = AP = BP
Side AB = √64 = 8
Side BP = √((a-4)² + b²)= 8
=> (a-4)² + b² = 64
=> b² = 64 - (a-4)²
Side AP = √((a+4)² + b²)= 8
=> (a+4)² + b²= 64
=> (a+4)² + 64 - (a-4)² = 64
=> 16a = 0
=> a = 0
b² = 64 - 16 = 48
=> b = √48 , -√48
The point P can be either (0,-√48) or (0,√48).
Slope of line segment AB = 0
Equation of line segment AB -
y = 0 , the line AB is the x-axis.
Distance of P from line AB = √48
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Answer:Hi Mohd. here's your answer :)