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Q.

The area of triangle formed by tangents at the parametric points $t_{1}, t_{2}$ and $t_{3}$ on $y^{2} = 4 a x$ is $k |(t_{1} - t_{2}) (t_{1} - t_{3}) (t_{3} - t_{1})|$ then K=

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a

$a^{2} / 2$

b

$a^{2}$

c

$2 a^{2}$

d

$4 a^{2}$

answer is A.

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Detailed Solution

We know that area of the triangle is

$\Rightarrow \frac{a^{2}}{2} |(t_{1} - t_{2}) (t_{2} - t_{3}) (t_{3} - t_{1})| ∴ K = \frac{a^{2}}{2}$

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The area of triangle formed by tangents at the parametric points t1,t2 and t3 on y2=4ax is kt1−t2t1−t3t3−t1 then K=