csat-suneung 2013 Q18

csat-suneung · South-Korea · csat__math-science 4 marks Conic sections Focal Chord and Parabola Segment Relations

For a natural number $n$, a line passing through the focus F of the parabola $y ^ { 2 } = \frac { x } { n }$ intersects the parabola at two points P and Q, respectively. If $\overline { \mathrm { PF } } = 1$ and $\overline { \mathrm { FQ } } = a _ { n }$, what is the value of $\sum _ { n = 1 } ^ { 10 } \frac { 1 } { a _ { n } }$? [4 points]
(1) 210
(2) 205
(3) 200
(4) 195
(5) 190

For a natural number $n$, a line passing through the focus F of the parabola $y ^ { 2 } = \frac { x } { n }$ intersects the parabola at two points P and Q, respectively.\\
If $\overline { \mathrm { PF } } = 1$ and $\overline { \mathrm { FQ } } = a _ { n }$, what is the value of $\sum _ { n = 1 } ^ { 10 } \frac { 1 } { a _ { n } }$? [4 points]\\
(1) 210\\
(2) 205\\
(3) 200\\
(4) 195\\
(5) 190

Paper Questions

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