Straight Lines
Collinearity
JEE Main 2022
Grade 11
Question:
For $\alpha_1, \alpha_2 \in \mathbb{R}$, the points $(\alpha, -3), (2, 0)$ and $(1, \alpha)$ are collinear for $\alpha \in \{\alpha_1, \alpha_2\}$. Find $\alpha_1^2 + \alpha_2^2$.
Step-by-Step Solution
Key Concept: Collinearity condition: the area of the triangle formed by the three points equals zero. This gives a quadratic in $\alpha$. Find $\alpha_1, \alpha_2$ using Vieta's formulas, then $\alpha_1^2 + \alpha_2^2$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: 10