csat-suneung 2024 Q29_geometry

csat-suneung · South-Korea · csat__math 4 marks Conic sections Focal Distance and Point-on-Conic Metric Computation
For a positive number $c$, there is a hyperbola with foci $\mathrm{F}(c, 0)$ and $\mathrm{F'}(-c, 0)$ and major axis length 6. Two distinct points $\mathrm{P}$ and $\mathrm{Q}$ on this hyperbola satisfy the following conditions. Find the sum of all values of $c$. [4 points] (가) Point P is in the first quadrant, and point Q is on line $\mathrm{PF'}$. (나) Triangle $\mathrm{PF'F}$ is isosceles. (다) The perimeter of triangle PQF is 28. 
For a positive number $c$, there is a hyperbola with foci $\mathrm{F}(c, 0)$ and $\mathrm{F'}(-c, 0)$ and major axis length 6. Two distinct points $\mathrm{P}$ and $\mathrm{Q}$ on this hyperbola satisfy the following conditions. Find the sum of all values of $c$. [4 points]\\
(가) Point P is in the first quadrant, and point Q is on line $\mathrm{PF'}$.\\
(나) Triangle $\mathrm{PF'F}$ is isosceles.\\
(다) The perimeter of triangle PQF is 28.
Paper Questions
Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q23_calculus Q23_geometry Q24 Q24_calculus Q24_geometry Q25 Q25_calculus Q25_geometry Q26 Q26_calculus Q26_geometry Q27 Q27_calculus Q27_geometry Q28 Q28_calculus Q28_geometry Q29 Q29_geometry Q30 Q30_geometry