Question

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.​

Answer 1

Answer:Hi Mohd. here's your answer :)

Answer 2

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