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Question

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 _____.


A

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B

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C

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D

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Solution

The correct option is A


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+t1t2t3t1t2t3t1t23)1×a2(t1t2t3+t21t2t21t3t1t2t3)+a2(t1t22+t1t2t3t1t2t3t22t3)]

=12a2[t21(t3t2)+t22(t1t3)+t23(t2t1)]

=12a2[t21(t2t3)+t22(t3t1)+t23(t1t2)]

Area can't be negative

Taking numerical value only

Area of triangle PQR=12a2[t21(t2t3)+t22(t3t1)+t23(t1t2)]


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