if A=(a2,2a),B=(1/a2,-2/a) and S=(1,0), then 1/SA+1/SB is equal to - Maths - Coordinate Geometry

Question

if A=(a2,2a),B=(1/a2,-2/a) and S=(1,0),
then 1/SA+1/SB is equal to

Ruchira Banka · Accepted Answer

A (a2, 2a)B (1a2, -2a)

S (1, 0)

SA = (a2 - 1)2 + (2a - 0)2 = a4 + 1 - 2a2 + 4a2 = 2a2 + a4 + 1 =
(a2 + 1)2 = a2 + 1

1SA= 1a2 + 1

SB = (1a2 - 1)2 + (-2a - 0)2 = 1a4 + 1 - 2a2 + 4a2 = 1a4 + 1 + 2a2
= (1a2 + 1)2 = 1a2 + 1 = 1 + a2a2

1SB = a21 + a21SA + 1SB = 1a2 + 1 + a2a2 + 1 = a2 + 1a2 + 1 = 1