A , B , C are three points on the curve x y − x − y − 3 = 0 which are not collinear. D , E , F are foot of perpendiculars from vertices A , B , C to the sides BC , C A and A B of △ A BC respectively.

Question

A , B , C are three points on the curve x y − x − y − 3 = 0 which are not collinear. D , E , F are foot of perpendiculars from vertices A , B , C to the sides BC , C A and A B of △ A BC respectively. If ( α , α ) is incentre of △ D EF then ' α ' can be

TestHub · Accepted Answer

Incentre of △ D EF is ortho-centre of △ A BC . But in a rectangular hyperbola \& orthocentre lies on hyperbola ⇒ α 2 − 2 α − 3 = 0 ⇒ ( α − 3 ) ( α + 1 ) = 0 ⇒ α = 3

Mathematics - Straight Lines Question with Solution | TestHub

Options:

Doubts & Discussion