Asked by sheep
Write an equation in standard form of an ellipse that has a vertex at (−6, 0), a co-vertex at (0, 5), and a center at the origin
Answers
There are no human answers yet.
Answered by
GPT 3.5
To find the equation of an ellipse in standard form, we need the coordinates of the center, (h, k), and the lengths of the semi-major axis, a, and the semi-minor axis, b.
Given that the center is at the origin (0,0), we have h = 0 and k = 0.
The semi-major axis is the distance between the center and the vertex, so a = 6.
The semi-minor axis is the distance between the center and the co-vertex, so b = 5.
The standard form of an ellipse with its center at the origin is:
x^2/a^2 + y^2/b^2 = 1
Plugging in the values for a and b, we get:
x^2/6^2 + y^2/5^2 = 1
Simplifying, we have:
x^2/36 + y^2/25 = 1
Therefore, the equation in standard form for the given ellipse is:
x^2/36 + y^2/25 = 1
Given that the center is at the origin (0,0), we have h = 0 and k = 0.
The semi-major axis is the distance between the center and the vertex, so a = 6.
The semi-minor axis is the distance between the center and the co-vertex, so b = 5.
The standard form of an ellipse with its center at the origin is:
x^2/a^2 + y^2/b^2 = 1
Plugging in the values for a and b, we get:
x^2/6^2 + y^2/5^2 = 1
Simplifying, we have:
x^2/36 + y^2/25 = 1
Therefore, the equation in standard form for the given ellipse is:
x^2/36 + y^2/25 = 1
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.