the foci of the ellipse given by the equation 100x2 + 25y2 = 2500?
x^2/25+y^2/100=1
To find the foci of the ellipse given by the equation 100x^2 + 25y^2 = 2500, you can follow these steps:
Step 1: Divide both sides of the equation by 2500 to simplify the equation:
x^2/25 + y^2/100 = 1
Step 2: Rewrite the equation in standard form, which is (x-h)^2/a^2 + (y-k)^2/b^2 = 1. We can see that a^2 = 25 and b^2 = 100. Thus, a = 5 and b = 10.
Step 3: The distance c from the center to the foci is given by c = √(a^2 - b^2). In this case, c = √(25 - 100) = √(-75) = √(-1) * √(25 * 3) = 5i√3.
Step 4: Since the center of the ellipse is at (0, 0), the foci will be at (0, c) and (0, -c). So, the foci of the ellipse are (0, 5i√3) and (0, -5i√3).
To find the foci of the ellipse given by the equation 100x^2 + 25y^2 = 2500, we can start by putting the equation in standard form for an ellipse.
The standard form equation for an ellipse centered at the origin is (x^2 / a^2) + (y^2 / b^2) = 1, where 'a' represents the semi-major axis length and 'b' represents the semi-minor axis length.
To convert the given equation into standard form, we need to divide both sides of the equation by 2500 to get:
(x^2 / 25) + (y^2 / 100) = 1
Now, let's compare this equation with the standard form equation:
(x^2 / a^2) + (y^2 / b^2) = 1
From the comparison, we can determine that the value of 'a' is 5 since a^2 = 25, and the value of 'b' is 10 since b^2 = 100.
The foci of an ellipse can be found using the formula c = √(a^2 - b^2), where 'c' represents the distance from the origin to the foci.
Substituting the values, we have:
c = √(5^2 - 10^2)
= √(25 - 100)
= √(-75)
= √(75 * -1)
= √75 * √-1
= √(3 * 25) * i
= 5√3 * i
Therefore, the foci of the given ellipse are at (0, 5√3) and (0, -5√3).
x^2/25 + y^2/100 = 1
the major axis is vertical.
a = 10
b = 5
c^2 = a^2-b^2 = 75
The foci are at (0,±c)