Question:
One possible condition for the three points \((a,b), (b,a)\) and \((a^2, -b^2)\) to be collinear, is
One possible condition for the three points \((a,b), (b,a)\) and \((a^2, -b^2)\) to be collinear, is
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Collinearity condition: slope between any two pairs is equal.
Updated On: Apr 20, 2026
- \(a - b = 2\)
- \(a + b = 2\)
- \(a = 1 + b\)
- \(a = 1 - b\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
\begin{vmatrix}
a & b & 1
b & a & 1
a^2 & -b^2 & 1 \end{vmatrix} = 0
Step 2: Detailed Explanation: \Delta = a(a + b^2) - b(b - a^2) + 1(-b^3 - a^3)
= a^2 + ab^2 - b^2 + a^2b - b^3 - a^3
= (a - b)(a - b - 1) = 0
a = b \text{ or } a - b = 1 \Rightarrow a = 1 + b
Step 3: Final Answer: a = 1 + b
b & a & 1
a^2 & -b^2 & 1 \end{vmatrix} = 0
Step 2: Detailed Explanation: \Delta = a(a + b^2) - b(b - a^2) + 1(-b^3 - a^3)
= a^2 + ab^2 - b^2 + a^2b - b^3 - a^3
= (a - b)(a - b - 1) = 0
a = b \text{ or } a - b = 1 \Rightarrow a = 1 + b
Step 3: Final Answer: a = 1 + b
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