Name the axis to which the major axis is parallel and find the center of
25(x+5)^(2)+4(y-3)^(2)=100
I think that the center is (-5,3). Is that correct?
I need help with finding out which axis the major axis is parallel to. I do not know how to do it.
center is correct
25(x+5)^(2)+4(y-3)^(2)=100
(x+5)^2 / 4 + (y-3)^2 / 25 = 1
(x+5)^2 / 2^2 + (y-3)^2 / 5^2 = 1
which is bigger , 5 or 2 ?
to make that easier look at
x^2/2^2 + y^2/5^2
5^2 is bigger.
You got it.
now what is x when y = 0 and what is y when x = 0 in
x^2/2^2 + y^2/5^2 = 1
???????????????????????
all I did was move the center to the origin.
x=2 and y=5
x = + or - 2 along x axis
y = + or - 5 along y axis
now which is longer ? :)
Draw x and y axis system and mark those points, then draw an ellipse through them !
To determine which axis the major axis is parallel to in an ellipse, you need to look at the equation of the ellipse and compare the coefficients of the squared terms of x and y.
In the given equation, 25(x+5)^(2) + 4(y-3)^(2) = 100, the squared terms are (x+5)^(2) and (y-3)^(2).
The coefficient of the squared term of x is 25, and the coefficient of the squared term of y is 4.
The major axis of the ellipse is parallel to the axis with the larger coefficient. In this case, the major axis is parallel to the y-axis because the coefficient of the squared term of y (4) is larger than the coefficient of the squared term of x (25).
So, the major axis of this ellipse is vertical and parallel to the y-axis.
Now, let's find the center of the ellipse.
The general form of the equation of an ellipse is (x-h)^(2)/a^(2) + (y-k)^(2)/b^(2) = 1, where (h, k) represents the coordinates of the center.
Comparing this general form with the given equation, we can see that the center is at the point (-5, 3). Therefore, your initial guess of the center is indeed correct.
To summarize:
- The major axis of the ellipse is parallel to the y-axis.
- The center of the ellipse is (-5, 3).