csat-suneung 2012 Q12

csat-suneung · South-Korea · csat__math-humanities 3 marks Stationary points and optimisation Geometric or applied optimisation problem

As shown in the figure, there are two points $\mathrm { A } ( - 1,0 )$ and $\mathrm { P } ( t , t + 1 )$ on the line $y = x + 1$. Let Q be the point where the line passing through P and perpendicular to the line $y = x + 1$ meets the $y$-axis. What is the value of $\lim _ { t \rightarrow \infty } \frac { \overline { \mathrm { AQ } } ^ { 2 } } { \overline { \mathrm { AP } } ^ { 2 } }$? [3 points]
(1) 1
(2) $\frac { 3 } { 2 }$
(3) 2
(4) $\frac { 5 } { 2 }$
(5) 3

As shown in the figure, there are two points $\mathrm { A } ( - 1,0 )$ and $\mathrm { P } ( t , t + 1 )$ on the line $y = x + 1$. Let Q be the point where the line passing through P and perpendicular to the line $y = x + 1$ meets the $y$-axis. What is the value of $\lim _ { t \rightarrow \infty } \frac { \overline { \mathrm { AQ } } ^ { 2 } } { \overline { \mathrm { AP } } ^ { 2 } }$? [3 points]\\
(1) 1\\
(2) $\frac { 3 } { 2 }$\\
(3) 2\\
(4) $\frac { 5 } { 2 }$\\
(5) 3

Paper Questions

Q1 Q2 Q3 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q24 Q25 Q26 Q27 Q28 Q29 Q30