How do you write an equation for an ellipse?
Understand the Problem
The question is asking for guidance on how to formulate an equation that represents an ellipse. This involves understanding the general form of the ellipse equation and the specific parameters that define it, like the lengths of the semi-major and semi-minor axes and the center of the ellipse.
Answer
(x^2 / a^2) + (y^2 / b^2) = 1 or ((x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
The final answer is (x^2 / a^2) + (y^2 / b^2) = 1 or ( (x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
Answer for screen readers
The final answer is (x^2 / a^2) + (y^2 / b^2) = 1 or ( (x - h)^2 / a^2) + ((y - k)^2 / b^2) = 1
More Information
The first form represents an ellipse centered at the origin, while the second form represents an ellipse centered at (h, k). The values of 'a' and 'b' are the distances from the center to the vertices along the x and y axes, respectively.
Tips
Ensure 'a' and 'b' represent the correct semi-major and semi-minor axes, and remember to center the ellipse at the correct point when dealing with non-origin centered ellipses.
