The area of the triangle formed by three points P { at1t2,a(t1+t2) },Q { at2t3,a(t2+t3) },R { at3t1,a(t3+t1) } is _____.
Given three points are
{at1t2,a(t1+t2)},{at2t3,a(t2+t3)},{at3t1,a(t3+t1)}
Area of triangle
12∣∣ ∣∣111at1t2at2t3at3t1a(t1+t2)a(t2+t3)a(t3+t1)∣∣ ∣∣
=12[a2(t2t23+t1t2t3−t1t2t3−t1t23)−1×a2(t1t2t3+t21t2−t21t3−t1t2t3)+a2(t1t22+t1t2t3−t1t2t3−t22t3)]
=12a2[t21(t3−t2)+t22(t1−t3)+t23(t2−t1)]
=−12a2[t21(t2−t3)+t22(t3−t1)+t23(t1−t2)]
Area can't be negative
Taking numerical value only
Area of triangle PQR=12a2[t21(t2−t3)+t22(t3−t1)+t23(t1−t2)]