Question

If the vertices of triangle ABC are A(at1^2,2at1),B(at2^2,2at2) and C(at3^2,2at3) respectively and O' is the orthocentre of triangle ABC,then find the coordinates of orthocentre of triangle O'BC

Answer 1

Given :  vertices of triangle ABC are A = ( at₁² , 2at₁) , B = ( at₂² , 2at₂) , C =  ( at₃² , 2at₃)

O' is the orthocentre of triangle ABC

To find : coordinates of orthocentre of triangle O'BC

Solution:

A = ( at₁² , 2at₁)

B = ( at₂² , 2at₂)

C =  ( at₃² , 2at₃)

Ortho center is the point where altitudes meets

Let say  AD , BE  & CF are altitudes intersecting at O'

AD ⊥  BC     => O'D ⊥  BC

BE ⊥ AC     => CE ⊥ BE  => CE ⊥ BO'

CF ⊥ AB     => BF ⊥ CF => BF ⊥ CO'

Now in triangle  O'BC

O'D  ,  CE  &  BF  are altitudes

meeting at A

Hence coordinates of orthocentre of triangle O'BC  = A = ( at₁² , 2at₁)

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