AP EAMCET Engineering 17 Sep 2020 Shift 2 Paper

We are given with a cubic equation which represents 3-lines.
Let lines have,
y−m1x=0;y−m2x=0
and y−m3x=0
Then, (y−m1x)(y−m2x)(y−m3x)=0
is the combined equations Which in this case is,
Which in this case is,
y3−6xy2+11x2y−6x3=0
By comparison we are able to put above equation are,
(y−x)(y−2x)(y−3x)=0
So, lines are,
L1⇒y−x=0
L2⇒y−2x=0
and L3⇒y=3x=0
Their intersection points with
x+y=1 are,
P≡x+y=1 and y−x=0
⇒‌‌P≡(‌

1

2

,‌

1

2

)
Q≡x+y=1 and y−2x=0
⇒‌‌Q≡(‌

1

3

,‌

2

3

)
R≡x+y=1 and y−3x=0
⇒‌‌R≡(‌

1

4

,‌

3

4

)
So, QP2+OQ2+OR2