Math, asked by ghostplasma11, 1 month ago

Q.22Δ OAB is formed by lines 2 - 4xy + 2 = 0 and the line x + y - 2 = 0. Find the equation of the median of the triangle drawn from O.​

Answers

Answered by Anonymous
13

Answer:

Let D be the midpoint of seg AB where A is (x

1

,y

1

) and B is (x

2

,y

2

)

Then D has coordinates (

2

x

1

+x

2

,

2

y

1

+y

2

)

The joint (combined) equation of the lines OA and OB is x

2

−4xy+y

2

=0 and the equation of the line AB is 2x+3y−1=0

∴ points A and B satisfy the equation 2x+3y−1=0 and x

2

−4xy+y

2

=0 simultaneously.

We eliminate x from the above equations, i.e. put x=

2

1−3y

in the equation x

2

−4xy+y

2

=0, we get,

∴(

2

1−3y

)

2

−4(

2

1−3y

)y+y

2

=0

∴(1−3y)

2

−8(1−3y)y+4y

2

=0

∴1−6y+9y

2

−8y+24y

2

+4y

2

=0

∴37y

2

−14y+1=0

The roots y

1

and y

2

of the above quadratic equation are the y− coordinates of the points A and B.

∴y

1

+y

2

=−

a

b

=

37

14

∴y− coordinates of D=

2

y

1

+y

2

=

37

7

Since D lies on the line AB, we can find the x− coordinate of D as

2x+3(

37

7

)−1=0

∴2x=1−

37

21

=

37

16

∴x=

37

8

∴D is (

37

8

,

37

7

)

∴ equation of the median OD is

8/37

x

=

3/37

y

i.e 7x−8y=0

hope it's helpful for you to learn

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