taiwan-gsat 2010 Q7

taiwan-gsat · Other · gsat__math 5 marks Conic sections Conic Identification and Conceptual Properties
7. Let the ellipses $\Gamma_{1}: \frac{x^{2}}{5^{2}} + \frac{y^{2}}{3^{2}} = 1$, $\Gamma_{2}: \frac{x^{2}}{5^{2}} + \frac{y^{2}}{3^{2}} = 2$, $\Gamma_{3}: \frac{x^{2}}{5^{2}} + \frac{y^{2}}{3^{2}} = \frac{2x}{5}$ have major axis lengths $l_{1}$, $l_{2}$, $l_{3}$ respectively. Which of the following options is correct?
(1) $l_{1} = l_{2} = l_{3}$
(2) $l_{1} = l_{2} < l_{3}$
(3) $l_{1} < l_{2} < l_{3}$
(4) $l_{1} = l_{3} < l_{2}$
(5) $l_{1} < l_{3} < l_{2}$
II. Multiple-Choice Questions (25 points)
Instructions: For questions 8 through 12, each of the five options is independent, and at least one option is correct. Select all correct options and mark them on the ``Answer Sheet''. No points are deducted for incorrect answers. Full marks (5 points) are awarded for all five options correct; 2.5 points are awarded if only one option is incorrect; no points are awarded if two or more options are incorrect.
& 4 & & 19 & 3 & & 29 & 2
7. Let the ellipses $\Gamma_{1}: \frac{x^{2}}{5^{2}} + \frac{y^{2}}{3^{2}} = 1$, $\Gamma_{2}: \frac{x^{2}}{5^{2}} + \frac{y^{2}}{3^{2}} = 2$, $\Gamma_{3}: \frac{x^{2}}{5^{2}} + \frac{y^{2}}{3^{2}} = \frac{2x}{5}$ have major axis lengths $l_{1}$, $l_{2}$, $l_{3}$ respectively. Which of the following options is correct?\\
(1) $l_{1} = l_{2} = l_{3}$\\
(2) $l_{1} = l_{2} < l_{3}$\\
(3) $l_{1} < l_{2} < l_{3}$\\
(4) $l_{1} = l_{3} < l_{2}$\\
(5) $l_{1} < l_{3} < l_{2}$

\section*{II. Multiple-Choice Questions (25 points)}
Instructions: For questions 8 through 12, each of the five options is independent, and at least one option is correct. Select all correct options and mark them on the ``Answer Sheet''. No points are deducted for incorrect answers. Full marks (5 points) are awarded for all five options correct; 2.5 points are awarded if only one option is incorrect; no points are awarded if two or more options are incorrect.