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Prove that the area of the triangle formed by the three normals to the parabola y^2 = 4ax at the points t1 ,t2 , and t3 is

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Prove that the area of the triangle formed by the three normals to the parabola y2 = 4ax at the points t1 ,t2 , and t3 is

1/2 a2|(t1 - t2)(t2 - t3)(t3 - t1)(t1 + t2 + t3)2|

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1 Answer

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Best answer

The vertices of the triangle are

Let these points be A, B and C, respectively. Therefore

Area of the ΔABC

= Absolute value of

= Absolute value of

= Absolute value of

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