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Question

The coordinates of the orthocentre of the triangle formed by the lines 2x23xy+y2=0 and x+y=1 is

A
(1,1)
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B
(12,12)
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C
(13,13)
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D
(14,14)
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Solution

The correct option is B (12,12)

2x23xy+y2=0

t=yx

t23t+2=0

t=3±982

t=3±12

t=2,1

And x+y=1 is third side.

Two sides of triangle
i.e. y=x and x+y=1 are p
erpendicular to each other.

So, orthocenter of triangle is intersection of

y=x & x+y=1 line

y=12=x

(12,12) is orthocentre.


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