Find the vertices, foci and eccentricity of the ellipse.Thank you
9x^2 + y^2 = 81
divide by 81
x^2/9 + y^2/81 = 1
then look at my reply to your other post for the same kind of question
http://www.jiskha.com/display.cgi?id=1354265681
thanks I got it right.
To find the vertices, foci, and eccentricity of an ellipse, we'll start by putting the given equation in standard form. The standard form of an ellipse with a horizontal major axis is given by:
(x-h)^2/a^2 + (y-k)^2/b^2 = 1
Where (h, k) represents the center of the ellipse, 'a' is the distance from the center to the vertex along the major axis, and 'b' is the distance from the center to the vertex along the minor axis.
Let's rewrite the given equation in standard form:
9x^2 + y^2 = 81
Dividing both sides by 81, we have:
x^2/81 + y^2/81 = 1
Now, we need to rewrite the equation with the same denominator for both x^2 and y^2 terms. Since 81 is a perfect square, we can rewrite it as (9^2):
x^2/9^2 + y^2/9^2 = 1
Comparing this with the standard form, we can see that the center of the ellipse is (h, k) = (0, 0), and the values of 'a' and 'b' are both 9.
Now, we can find the vertices, foci, and eccentricity:
The vertices: The vertices are the points where the ellipse intersects the major axis. Since the major axis is along the x-axis, the vertices will be (±a, k). In this case, the vertices are (±9, 0): V1(9, 0) and V2(-9, 0).
The foci: The foci are the points inside the ellipse that determine its shape. The distance from the center to each focus, denoted by 'c', can be found using the formula c = sqrt(a^2 - b^2). In this case, 'a' and 'b' are both 9. Thus, c = sqrt(9^2 - 9^2) = 0.
The eccentricity: The eccentricity, denoted by 'e', is a measure of how elongated the ellipse is. It can be calculated using the formula e = c/a. In this case, c = 0 and a = 9. Therefore, the eccentricity e = 0/9 = 0.
In summary:
- The center of the ellipse is (0, 0).
- The vertices are V1(9, 0) and V2(-9, 0).
- The foci are located at F1(0, 0) and F2(0, 0).
- The eccentricity of the ellipse is 0.