ABC is a variable triangle such that A is 1-2 and B and C on the line y - x - - - Then the locus of the orthocenter of - ABC is

The correct option is A x + y = 0 M_BC slope of BC × slope of AD = 1 +1× M_AD= 1 M_AD= 1 Equation AD y 2= 1(x 1) y 2= x+ ...

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Standard XII

Mathematics

Formation of a Differential Equation from a General Solution

ABC is a vari...

Question

ABC is a variable triangle such that A is $(1, 2)$ and B and C on the line $y = x + λ$ . Then the locus of the orthocenter of $Δ A B C$ is

x + y = 0

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x - y = 0

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

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x + y = 3

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Solution

The correct option is A $x + y = 0$
$M_{B C}$ slope of BC $\times$ slope of AD $= - 1$
$+ 1 \times M_{A D} = - 1$
$M_{A D} = - 1$
Equation AD
$y - 2 = - 1 (x - 1)$
$y - 2 = - x + 1$
$x + y = 3$ .

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

The correct option is A x+y=0MBC slope of BC× slope of AD=−1+1×MAD=−1MAD=−1Equation ADy−2=−1(x−1)y−2=−x+1x+y=3.

ABC is a variable triangle such that A is $(1, 2)$ and B and C on the line $y = x + λ$ . Then the locus of the orthocenter of $Δ A B C$ is

The correct option is A $x + y = 0$
$M_{B C}$ slope of BC $\times$ slope of AD $= - 1$
$+ 1 \times M_{A D} = - 1$
$M_{A D} = - 1$
Equation AD
$y - 2 = - 1 (x - 1)$
$y - 2 = - x + 1$
$x + y = 3$ .