A whispering gallery is an elliptical- shaped room with a dome-shaped ceilling. If two people stand at the foci of the ellipse and whisper, they can hear each other, but others cannot. The maximum length and width of such a hall are 100m and 80m, respectively. Which of hte following equations models the shape of the hall ?

Question

A whispering gallery is an elliptical- shaped room with a dome-shaped ceilling. If two people stand at the foci of the ellipse and whisper, they can hear each other, but others cannot. The maximum length and width of such a hall are 100m and 80m, respectively. Which of hte following equations models the  shape of the hall ?

Accepted Answer

গ. $\frac{x^{2}}{2500} + \frac{y^{2}}{1600} = 1$

ব্যাখ্যা: উপবৃত্তাকার হলের সর্বোচ্চ দৈর্ঘ্য $2a = 100	ext{ m} \implies a = 50$ এবং প্রস্থ $2b = 80	ext{ m} \implies b = 40$। সুতরাং, উপবৃত্তটির সমীকরণ হবে $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \implies \frac{x^2}{50^2} + \frac{y^2}{40^2} = 1 \implies \frac{x^2}{2500} + \frac{y^2}{1600} = 1$।

উচ্চতর গণিত ২য় পত্র প্রশ্ন

সম্পর্কিত প্রশ্ন