csat-suneung 2012 Q11

csat-suneung · South-Korea · csat__math-science 3 marks Conic sections Triangle or Quadrilateral Area and Perimeter with Foci

For a rhombus ABCD with side length 10, an ellipse with diagonal BD as the major axis and diagonal AC as the minor axis has a distance between the two foci of $10 \sqrt { 2 }$. What is the area of rhombus ABCD? [3 points]
(1) $55 \sqrt { 3 }$
(2) $65 \sqrt { 2 }$
(3) $50 \sqrt { 3 }$
(4) $45 \sqrt { 3 }$
(5) $45 \sqrt { 2 }$

For a rhombus ABCD with side length 10, an ellipse with diagonal BD as the major axis and diagonal AC as the minor axis has a distance between the two foci of $10 \sqrt { 2 }$. What is the area of rhombus ABCD? [3 points]\\
(1) $55 \sqrt { 3 }$\\
(2) $65 \sqrt { 2 }$\\
(3) $50 \sqrt { 3 }$\\
(4) $45 \sqrt { 3 }$\\
(5) $45 \sqrt { 2 }$

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