csat-suneung 2006 Q7

csat-suneung · South-Korea · csat__math-science 3 marks Conic sections Triangle or Quadrilateral Area and Perimeter with Foci
The figure on the right shows 6 ellipses, each with a side of a regular hexagon ABCDEF with side length 10 as the major axis, and with equal minor axis lengths. As shown in the figure, the sum of the areas of 6 triangles formed by a vertex of the regular hexagon and the foci of the two adjacent ellipses is $6 \sqrt { 3 }$. What is the length of the minor axis of the ellipse? [3 points]
(1) $4 \sqrt { 2 }$
(2) 6
(3) $4 \sqrt { 3 }$
(4) 8
(5) $6 \sqrt { 2 }$ 
The figure on the right shows 6 ellipses, each with a side of a regular hexagon ABCDEF with side length 10 as the major axis, and with equal minor axis lengths. As shown in the figure, the sum of the areas of 6 triangles formed by a vertex of the regular hexagon and the foci of the two adjacent ellipses is $6 \sqrt { 3 }$. What is the length of the minor axis of the ellipse? [3 points]\\
(1) $4 \sqrt { 2 }$\\
(2) 6\\
(3) $4 \sqrt { 3 }$\\
(4) 8\\
(5) $6 \sqrt { 2 }$
Paper Questions
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