Find the co-vertices of the ellipse defined by the equation shown below.
25x^2+4y^2-150x+8y+129=0
To find the co-vertices of an ellipse, we need to identify the center of the ellipse and its semi-axes (a and b).
First, we need to simplify the given equation by completing the square for both x and y terms:
25(x^2 - 6x + 9) + 4(y^2 + 2y + 1) = 100
Dividing by 100 on both sides, we get:
(x - 3)^2/4 + (y + 1/2)^2/25 = 1
Now we can see that the center of the ellipse is at (3, -1/2), and the semi-axes are a = 2 and b = 5.
The co-vertices are located on the minor axis (the y-axis in this case) and their distance from the center is b. Therefore, the coordinates of the co-vertices are (3, -1/2 + 5) = (3, 4.5) and (3, -1/2 - 5) = (3, -5.5).
So the co-vertices are (3, 4.5) and (3, -5.5).
your wrong
I'm sorry to hear that. Could you please provide me with more information or tell me how I can assist you?
maybe try to ound to the nearest tenth.
Certainly, I apologize for not rounding earlier.
Using the same method described earlier, we find that the center of the ellipse is at (3, -1/2), and that the semi-axes are a = 2 and b = 5.
The co-vertices are located on the minor axis (the y-axis in this case) and their distance from the center is b. Therefore, the coordinates of the co-vertices are (3, -1/2 + 5) = (3, 4.5) and (3, -1/2 - 5) = (3, -5.5).
Rounding to the nearest tenth, the co-vertices are approximately (3, 4.5) and (3, -5.5).
Find the co-vertices of the ellipse defined by the equation shown below.
9x^(2)+4y^(2)-36x+8y+4=0
To find the co-vertices of an ellipse, we need to identify the center of the ellipse and its semi-axes (a and b).
First, we need to simplify the given equation by completing the square for both x and y terms:
9(x^2 - 4x + 4) + 4(y^2 + 2y + 1) = 4 + 36
Dividing by 36 on both sides, we get:
(x - 2)^2/4 + (y + 1/2)^2/9 = 1
Now we can see that the center of the ellipse is at (2, -1/2), and the semi-axes are a = 2 and b = 3.
The co-vertices are located on the minor axis (the y-axis in this case) and their distance from the center is b. Therefore, the coordinates of the co-vertices are (2, -1/2 + 3) = (2, 2.5) and (2, -1/2 - 3) = (2, -4).
So the co-vertices are (2, 2.5) and (2, -4).