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JEE MATHEMATICS MCQ: 2D GEOMETRY SYSTEM

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Application +4 | -1
Let the area of the triangle with vertices A(1,α),    B(α,0)   and     C(0,α)A(1,\alpha ),\,\,\,\,B(\alpha ,0)\,\,\,{\text{and}}\,\,\,\,\,C(0,\alpha ) be 4 sq units. If the points (α,−α),   (−α,α)    and   (α2,β)(\alpha , - \alpha ),\,\,\,( - \alpha ,\alpha )\,\,\,\,{\text{and}}\,\,\,({\alpha ^2},\beta ) are collinear, then β\beta is equal to
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Correct option: C
-64
Option C (-64) is correct because by calculating the area of the triangle and using the collinearity condition, we can find the value of β\beta.

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