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Zetta Paper 1 · Q9

Paper 1Geometry

A circle of radius rr is dropped into the curve y=x2y=x^2 such that it only touches the curve. The circle's centre is (0,c)(0,c). Express cc in terms of rr. Diagram for question 9

A1+2r22\frac{1+2r^2}{2}
B1−4r24\frac{1-4r^2}{4}
C4rr2−2\frac{4r}{r^2-2}
Dr24−1\frac{r^2}{4}-1
E1+4r24\frac{1+4r^2}{4}
F1−6r22\frac{1-6r^2}{2}
Gr3−r4\frac{r^3-r}{4}

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