Question

The orthocentre of the triangle with vertices at A(0, 0), B(a, 0), C (0, b) is

Answer 1

Answer:

The plane of the triangle is x/a+y/b+z/c=1

Let O(α,β,y) be the orthocenter

drs of OA are α−a,β,y

drs of BC are o,−b,c

OA⊥BC⇒βb=yc

OB⊥CA⇒αa=yc

∴αa=βb=yc=k

2

(say)

o(α,β,y) lies on the plane

∴

a

α

+

b

β

+

c

y

=1⇒

k

2

1

=

a

2

1

+

b

2

1

+

c

2

1

The orthocentre is (

a

k

2

,

b

k

2

,

c

k

2

)

solution

Step-by-step explanation:

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