Question

Find the value of x, y if the distance of the point (x, y) from (-3,0) as well as from (3,0) are 4.

Answer 1

The distance between (x, y) from (-3, 0) is √[(x + 3)2 + y2]   
 √[(x + 3)2 + y2] = 4
[(x + 3)2 + y2] = 16
x2 + y2 + 6x  - 7 = 0  ... (1)
The distance between (x, y) from (3, 0) is √[(x - 3)2 + y2]    
√[(x - 3)2 + y2] = 4
[(x - 3)2 + y2] = 16
x2 + y2 - 6x  - 7 = 0  ... (2)
From (1) and (2) we get
6x  - 7 = - 6x  - 7
x = 0
Put x = 0 in (1) we get y = √7