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tmua.me Extreme Set B Paper 2 · Q17

Paper 2Algebra

A point PP lies on the parabola y=x2y=x^2. Its reflections in the three lines

x=0,y=0,3x+2y=12x=0,\qquad y=0,\qquad 3x+2y=12

are three distinct collinear points.

What is the sum of the reciprocals of the xx-coordinates of all possible points PP?

A−54-\dfrac54
B−1-1
C−34-\dfrac34
D−14-\dfrac14
E14\dfrac14
F54\dfrac54

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