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Question: The tangent to the parabola y<sup>2</sup> = 4ax at P(t<sub>1</sub>) and Q(t<sub>2</sub>) intersect a...

The tangent to the parabola y2 = 4ax at P(t1) and Q(t2) intersect at R. The area of ∆PQR is

A

12a2(t1−t2)2\frac{1}{2}a^{2}(t_{1} - t_{2})^{2}

B

12a2(t1−t2)\frac{1}{2}a^{2}(t_{1} - t_{2})^{}

C

12a2(t1−t2)3\frac{1}{2}a^{2}(t_{1} - t_{2})^{3}

D

12a2(t1+t2)3\frac{1}{2}a^{2}(t_{1} + t_{2})^{3}

Answer

12a2(t1−t2)3\frac{1}{2}a^{2}(t_{1} - t_{2})^{3}

Explanation

Solution

The point of intersection of tangents at P(t1­) and Q(t2) is (at1t2, a(t1+t2)) = R

We can prove that the area of triangle PQR =12a2(t1−t2)3\frac{1}{2}a^{2}(t_{1} - t_{2})^{3}