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Question

If xāˆ’2y+4=0 and 2x+yāˆ’5=0 are the sides of an isosceles triangle having area 10 sq. units the equation of third side is

A
3xy=9
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B
3xy11=0
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C
x3y=19
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D
3xy+15=0
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Solution

The correct options are
A 3xy=9
B 3xy11=0
Given sides
x2y+4=0-----(1) and
2x+y5=0-----(2)
from eq (1) and (2) we get intersecting point
I(65,135)
Eq of angle bisector of given lines
x2y+4=±(2x+y5)
on solving we get
x+3y=9 and 3xy=1
Side BC will be parallel to these bisectors.Let
AD=a where D is foot of perpendicular
AB=a2 and area of ΔABC is
12×(a2)2=a2=10
a=10
Let eq of BC be x+3y=λ
10=65395λ10λ=1,19
Eq of BC is x+3y=1 or x+3y=19
If eq of BC is 3xy=λ
10=185135λ10λ=9,11
Eq of BC is 3xy=9 or 3xy=11

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