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A B C is a variable triangle such that A...

`A B C` is a variable triangle such that `A` is (1,2) and `B` and `C` lie on line `y=x+lambda` (where `lambda` is a variable). Then the locus of the orthocentre of triangle `A B C` is `(x-1)^2+y^2=4` `x+y=3` `2x-y=0` (d) none of these

A

x+y=0

B

x-y=0

C

`x^(2) + y^(2)=4`

D

x+y=3

Text Solution

Verified by Experts

The correct Answer is:
D
As the altitude from A is fixed and the orthocenter lies on the altitude, x+y=3 is the required locus.
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