show that the points (at1^2 ,2at1) , (at2^2,2at2) , (a,0) are colinear if t1* t2 = -1
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Very Nice Question Sir
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Area of the triangle formed by these three points must be since they are collinear.
Δ = 1/2 | at1² (2at2) + at2² (-2at1) + a(2a)(t1-t2) |
= 1/2 | 2a² t1² t2 - 2a² t1 t2² + 2a² (t1-t2) |
= a² | t1²t2 - t1t2² + t1 - t2 |
= a² | t1t2(t1-t2) + (t1-t2) |
= a² | (t1-t2) (t1t2 -1)|
= a² | (t1-t2) (-1 -1)|
= a² | (t1-t2) (-2)|
Δ = 1/2 | at1² (2at2) + at2² (-2at1) + a(2a)(t1-t2) |
= 1/2 | 2a² t1² t2 - 2a² t1 t2² + 2a² (t1-t2) |
= a² | t1²t2 - t1t2² + t1 - t2 |
= a² | t1t2(t1-t2) + (t1-t2) |
= a² | (t1-t2) (t1t2 -1)|
= a² | (t1-t2) (-1 -1)|
= a² | (t1-t2) (-2)|
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there is ur answer.........
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