Can anyone help me with this problem step by step please...
Find the area inside the ellipse in the xy-plane determined by the given equation
x^2 y^2
____ + ___ =1
10 25
the area of
x^2/a^2 + y^2/b^2 = 1 is πab
http://www.math.hmc.edu/funfacts/ffiles/10006.3.shtml
so for yours
a^2 = 10, a = √10
b^2 = 25, b = 5
area = 5√10π
Reiny:
You are sincerely an angel. I so appreciate that you take the time to do this, to help people such as myself understand Math a whole lot better, and assist with problems we struggle with sometimes until 4am in the morning. Thank you, Thank you, thank you!...I do appreciate your time
To find the area inside the ellipse determined by the given equation, you can follow these steps:
Step 1: Rewrite the equation in a standard form.
The equation of the ellipse is in the form:
(x^2/a^2) + (y^2/b^2) = 1,
where 'a' and 'b' are the semi-major and semi-minor axes of the ellipse.
In this case, we have:
(x^2/10) + (y^2/25) = 1.
Step 2: Find the values of 'a' and 'b'.
Comparing the given equation with the standard form, we can see that a^2 = 10 and b^2 = 25.
Taking the square root of both a^2 and b^2, we find that a = √10 and b = 5.
Step 3: Calculate the area of the ellipse.
The formula to find the area of an ellipse is given by:
Area = π * a * b.
Substituting the values of a and b, we get:
Area = π * √10 * 5.
To calculate the numerical value, you can use a calculator or approximate √10 as 3.16 and substitute it into the formula:
Area ≈ 3.16 * 5 * π.
So, the area inside the ellipse, as determined by the given equation, is approximately 15.8π, or 49.35 square units.