MHT CET 2017 Math Solved Paper

(d)

Since, 0(0,0), A(1,2) and B(3,4) are the vertices of ΔOAB.
Consider that OP and OD are altitude and median of ΔOAB, respectively.
Then, Coordinates of D
=(

1+3

2

,

2+4

2

)=(2,3)
So, equation of OD is (y−0)= (

3−0

2−0

)(x−0)
Hence, y =

3

2

x ⇒ 3x - 2y = 0
Now, slope of OP =

−1

Slope‌of‌AB

−1

( 3−1 4−2 )

=−1 [As,OP⊥AB]
=

1

( 3−1 4−2 )

=−1
∴ Equation of OP is (y - 0) = -1 (x - 0)
∴ y = - x ⇒ x + y = 0
Hence, joint equation of OP and OD is:
(x + y)(3x - 2y) = 0
⇒ 3x2+xy+y2 = 0