Question

The points (at₁², 2at₁), (at₂², 2at₂) and (a, 0) will be collinear, if-

• A. t₁t₂ = 1
• B. t₁t₂ = – 1
• C. t₁ + t₂ = 1
• D. t₁ + t₂ = –1

Answer 1

Answer: (B)

t₁t₂ = – 1

Answer 2

$\left| \begin{matrix} at_{1}^{2} & 2at_{1} & 1 \\ at_{2}^{2} & 2at_{2} & 1 \\ a & 0 & 1 \end{matrix} \right|$ = 0

Ž $\left| \begin{matrix} t_{1}^{2} & t_{1} & 1 \\ t_{2}^{2} & t_{2} & 1 \\ 1 & 0 & 1 \end{matrix} \right|$ = 0

Ž t₁²t₂ – t₁ (t₂² – 1) + (– t₂) = 0

Ž t₁²t₂ – t₁t₂² + t₁ – t₂ = 0

Ž t₁t₂ (t₁ – t₂) + 1 (t₁ – t₂) = 0

Ž (t₁ – t₂) (t₁t₂ + 1) = 0

Ž t₁t₂ = – 1