Parabola

Given, parabola is y2=x and t1=2t2=−4 and t3=6.
So, intersection of tangents at t1 and t2, then tangents are 2y=x+1 and −4y=x+4
Solving these two equations, we get y=(‌

−1

2

) and x=−2
So, point L=(−2,−‌

1

2

)
Now, intersection of tangents at t2=−4 and t3=6, then tangents are
−4y=x+4,6y=x+9
Solving these two,
we get x=−6,y=‌

1

2

So, print M=(−6,‌

1

2

)
Now, intersection of tangents at t1=2 and t3=6, so tangents are 2y=x+1 and 6y=x+9
Solving these two equation, we get x=3,y=2
So, point N=(3,2)
Area of triangle with vertices L(−2,−‌

1

2

),M(−6,‌

1

2

) and N(3,2) is
‌ Area ‌‌=|‌

1

2

|‌begin‌array‌ccc−2‌−‌

1

2

‌1
−6‌‌

1

2

‌1||
3‌2‌1
‌=|‌

−15

2

|=7.5