Writing the Equation of an Ellipse from its Graph | Precalculus

Finding the Center of the Ellipse

• 🎯 The x-coordinate of the center is found by averaging the minimum and maximum x-values (-4 and 8), resulting in 2.
• 🎯 The y-coordinate of the center is found by averaging the minimum and maximum y-values (1 and 7), resulting in 4.
• 📍 Therefore, the center of the ellipse is at the coordinate point (2, 4).

Determining the Radii

• 📏 The minor radius (or semi-minor axis) is the shortest distance from the center to the ellipse's edge. In this case, it is 3 units.
• 📏 The major radius (or semi-major axis) is the longest distance from the center to the ellipse's edge. In this case, it is 6 units.

Constructing the Ellipse Equation

• 📝 The standard equation of an ellipse is derived using the center coordinates and the radii.
• 🔑 For the x-component, use (x - center_x)^2 divided by the square of the radius along the x-axis (major radius squared: 6^2 = 36).
• 🔑 For the y-component, use (y - center_y)^2 divided by the square of the radius along the y-axis (minor radius squared: 3^2 = 9).
• ✅ The final equation for this ellipse is (x - 2)^2 / 36 + (y - 4)^2 / 9 = 1.