A B C is a variable triangle such that A is (1,2), and B and C lie on the line y=x+λ(λ is a variable). Then the locus of the or thocenter of triangle A B C is

Question

A B C is a variable triangle such that A is (1,2), and B and C lie on the line y=x+λ(λ is a variable). Then the locus of the or thocenter of triangle A B C is (A) x+y=0 (B) x-y=0 (C) x2+y2=4 (D) x+y=3

Tardigrade Admin · Accepted Answer

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

Q. $A BC$ is a variable triangle such that $A$ is $(1, 2)$ , and $B$ and $C$ lie on the line $y = x + λ (λ$ is a variable). Then the locus of the or thocenter of $△ A BC$ is

$x + y = 0$

$x - y = 0$

$x^{2} + y^{2} = 4$

$x + y = 3$

As the altitude from $A$ is fixed and the orthocenter lies on the altitude, $x + y = 3$ is the required locus.

Q. ABC is a variable triangle such that A is (1,2), and B and C lie on the line y=x+λ(λ is a variable). Then the locus of the or thocenter of △ABC is

x+y=0

x−y=0

x2+y2=4

x+y=3