tmua.me Extreme Set B Paper 1 · Question 12

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tmua.me Extreme Set B Paper 1 · Q12

Paper 1Geometry

The lines

L_1:\ y=mx+1,\qquad L_2:\ y=mx-2

each meet the curve $y=x^2$ at two distinct points. The points on $L_1$ are $A$ and $B$ , and those on $L_2$ are $C$ and $D$ .

The area bounded by the segment $AB$ and the curve is eight times the area bounded by the segment $CD$ and the curve.

What is the value of $AB\cdot CD$ ?

8

8\sqrt{13}

52

208

104

416

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