Solve.
-The area of an ellipse given by the equation $\frac{(\mathrm{x}-\mathrm{h})^{2}}{\mathrm{a}^{2}}+\frac{(\mathrm{y}-\mathrm{k})^{2}}{\mathrm{~b}^{2}}=1$ is $\pi \mathrm{ab}$. A small park in the shape of an ellipse covers an area of 1432.57 square meters. The park measures 48 meters from east to west, what is the distance from north to south?
A) $38 \mathrm{~m}$
B) $576 \mathrm{~m}$
C) $361 \mathrm{~m}$
D) $48 \mathrm{~m}$

Question

Quizplus · Accepted Answer

The distance from east to west (48 meters) represents the major axis (2a) of the ellipse. Thus, $a = 24$ meters. Given the area $\pi ab = 1432.57$, we can solve for $b$: $1432.57 = \pi \times 24 \times b$. Solving for $b$ gives approximately $19$ meters. Since $b$ represents the semi-minor axis, the total distance from north to south (the minor axis) is $2b = 38$ meters.

Solve -The Area of an Ellipse Given by the Equation (x−h)2a2+(y−k)2 b2=1\frac{(\mathrm{x}-\mathrm{h})^{2}}{\mathrm{a}^{2}}+\frac{(\mathrm{y}-\mathrm{k})^{2}}{\mathrm{~b}^{2}}=1a2(x−h)2​+ b2(y−k)2​=1

Solve
-The Area of an Ellipse Given by the Equation $\frac{(\mathrm{x}-\mathrm{h})^{2}}{\mathrm{a}^{2}}+\frac{(\mathrm{y}-\mathrm{k})^{2}}{\mathrm{~b}^{2}}=1$