If the point on the y axis which is equidistance from the point (5,-2)

1.	If the point on the y axis which is equidistance from the point (5,-2)and (-3,2)
Answer» Let the given points be A(5, -2 ) and B(-3, 2) and let the required point be P(x, 0). Then,PA = PB\xa0{tex}\\Rightarrow{/tex}\xa0PA2\xa0= PB2{tex}\\Rightarrow{/tex}\xa0(x - 5)2\xa0+ (0 + 2)2= (x + 3)2\xa0+ (0 - 2)2{tex}\\Rightarrow{/tex}\xa0(x - 5)2\xa0+ 4 = (x + 3)2 + 4{tex}\\Rightarrow{/tex}\xa0(x - 5)2 - (x + 3)2 =0{tex}\\Rightarrow{/tex}\xa0(x 2 -10x + 25) - (x2 + 6x + 9)=0{tex}\\Rightarrow{/tex}\xa0-16x + 16 =0{tex}\\Rightarrow{/tex}\xa016x = 16\xa0{tex}\\Rightarrow{/tex}\xa0x = 1.Hence, the required point is P(1, 0).

Discussion