Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the ellipse. How far from the center of the ellipse will the spots be located?
A.2 feet
B.4 feet
C.3 feet
D.2.5 feet
E.3.5 feet
3.5 feet
To find the distance from the center of the ellipse to the foci, we can use the formula for the distance from the center to the foci of an ellipse:
c^2 = a^2 - b^2
Where:
a = semi-major axis (half the width of the ellipse)
b = semi-minor axis (half the maximum height of the ellipse)
c = distance from the center to the foci
In this case, the width of the ellipse is 5 feet, so the semi-major axis (a) is 5/2 = 2.5 feet. The maximum height of the ellipse is 3 feet, so the semi-minor axis (b) is 3/2 = 1.5 feet.
Now, let's plug the values into the formula:
c^2 = (2.5)^2 - (1.5)^2
c^2 = 6.25 - 2.25
c^2 = 4
To find the value of c, we take the square root of both sides:
c = 2
Therefore, the distance from the center of the ellipse to the foci is 2 feet.
So, the correct answer is A. 2 feet.
The semi-axes are 2.5 and 3
a^2 = b^2 + c^2
9 = 6.25 + c^2
c^2 = 2.75
c = 1.658
Either I have misinterpreted the details, or something's wrong here.
Oscar Corporation is planning to construct an elliptical gate at its headquarters. The width of the ellipse will be 5 feet across and its maximum height along the center will be 3 feet. The company wants to place two bright spots at the foci of the ellipse. How far from the center of the ellipse will the spots be located?
A.2 feet
B.4 feet
C.3 feet
D.2.5 feet
E.3.5 feet