If the medians AD and BE of the triangle with vertices A(0, b), B (0, 0) and C (a, 0) are perpendicular,then an equation of the line through (a, b) perpendicular to AC is

Slope of AD =b−00−a/2=−2baSlope of BE=b/2a/2=baSince AD and BE are perpendicular −2ba⋅ba=−1 ⇒ a2=2b2               (i)  Slope of AC is – b/a ∴ Equation of the line through (a, b) perpendicular to AC isy−b=cb(x−a)⇒ ax−by=a2−b2⇒±2bx−by=b2 from (i)±2x−y=b ⇒ y=±2x−bSo an equation of required line is y=2x−b