Coordinate Geometry Question 165
The vertices of a triangle are $ A $, $ B $, and $ C $.
[at_1t_2,a(t_1+t_2)], $
$ [a t_2 t_3,a(t_2+t_3)] $ , $ [a t_3 t_1,a(t_3+t_1)] $ , then the coordinates of its orthocentre are [IIT 1983]
Options:
A) $ [a,a(t_1+t_2+t_3+t_1t_2t_3)] $
B) $ [-a,a(t_1+t_2+t_3+t_1t_2t_3)] $
C) $ [-a(t_1+t_2+t_3+t_1t_2t_3),a] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
$ \Rightarrow 8(x^{2}+y^{2})-36y-2x+35=0 $ Therefore, perpendicular from point third $ t_2x+y=a[t_1t_2t_3+t_1+t_3] $ and perpendicular from point first $ t_1x+y=a[t_1t_2t_3+t_1+t_2] $
$ x=-a,y=a[t_1t_2t_3+t_1+t_2+t_3] $ .
BETA
