Solve.
-An elliptical bicycle path is constructed in a local park. The equation of the ellipse that represents the path, in yards, is given by $\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=1$. What are the length and the width of the bicycle path?
A) length: $70 \mathrm{yd}$; width: $130 \mathrm{yd}$
B) length: $130 \mathrm{yd}$; width: $70 \mathrm{yd}$
C) length: $35 \mathrm{yd}$; width: $65 \mathrm{yd}$
D) length: $65 \mathrm{yd}$; width: $35 \mathrm{yd}$

Question

Quizplus · Accepted Answer

The equation of the ellipse is given in the form $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $2a$ is the length of the major axis and $2b$ is the length of the minor axis. Here, $a^2 = 1225$ and $b^2 = 4225$, so $a = 35$ yards and $b = 65$ yards. Therefore, the length of the path is $2b = 130$ yards and the width is $2a = 70$ yards.

Solve -An Elliptical Bicycle Path Is Constructed in a Local x21225+y24225=1\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=11225x2​+4225y2​=1

Solve
-An Elliptical Bicycle Path Is Constructed in a Local $\frac{\mathrm{x}^{2}}{1225}+\frac{\mathrm{y}^{2}}{4225}=1$