Please help-What is the equation of the ellipse with foci (0,6), (0,-6) and co-vertices (2,0),(-2,0)
Please explain the steps because I have 5 to do for homework-Thank you-I'm really stuck on this
I thought the answer would be x^2/4 + y^2/40 = 1 but that can't be because the choices are:
x^2/1 + y^2/40 = 1 or x^2/1 + y^2/36
I'm really confused
I forgot to put that I think b= 2
c=6, so therefore
a^2-2^2 = 6^2
so a= 40, that' how I got to my equation
Your answer is correct.
It can't be correct my equation because that isn't a choice I was given-that's what I don't understand-thanks for trying to help though
Jodi,my answer was exactly identical to
yours.
To find the equation of an ellipse with given foci and co-vertices, we need to use the following formula:
c^2 = a^2 - b^2
Where:
- c is the distance from the center of the ellipse to each focus
- a is the distance from the center of the ellipse to each vertex
- b is the distance from the center of the ellipse to each co-vertex
Let's follow these steps to find the equation:
Step 1: Identify the necessary values
- The foci are given as (0, 6) and (0, -6). This means the distance from the center to each focus is 6.
- The co-vertices are given as (2, 0) and (-2, 0). This means the distance from the center to each co-vertex is 2.
Step 2: Find the value of a
Since a is the distance from the center to each vertex, we can observe that the distance from the center to each vertex is the same as the distance from the center to each focus, which is 6. Therefore, a = 6.
Step 3: Find the value of c
Since c is the distance from the center to each focus, we already know that c = 6.
Step 4: Find the value of b
To find b, we can use the formula:
c^2 = a^2 - b^2
Substituting the values we have:
6^2 = 6^2 - b^2
36 = 36 - b^2
b^2 = 0
Since b^2 = 0, this means that b = 0.
Step 5: Write the equation of the ellipse
Now that we have the values of a and b, we can write the equation of the ellipse, in the form:
x^2/a^2 + y^2/b^2 = 1
Substituting the values we found:
x^2/6^2 + y^2/0 = 1
However, we cannot divide by 0, so we must reconsider our approach. The equation x^2/4 + y^2/40 = 1 cannot be correct since the value of b should not be 0.
Let's check the other choices:
- x^2/1 + y^2/40 = 1
- x^2/1 + y^2/36 = 1
To determine which equation is correct, we need to compare the values we found for a and b with the given choices.
Since a = 6, none of the choices have a match.
Therefore, there may be an error in the given options, or a mistake in the question.
To resolve this confusion, it is recommended to double-check the given information or consult with your instructor for clarification.