Final answer:
To sketch the ellipse described by the equation x²/49 + y²/25 = 1, we can use the properties of ellipses. The equation represents an ellipse with the center at the origin (0,0), a major axis of length 2a = 14, and a minor axis of length 2b = 10. Plot the center and points on the x-axis, and connect them to sketch the ellipse.
Step-by-step explanation:
An ellipse is a closed curve with two foci. To sketch the ellipse described by the equation x²/49 + y²/25 = 1, we can use the properties of ellipses. The equation x²/49 + y²/25 = 1 represents an ellipse with the center at the origin (0,0), a major axis of length 2a = 14, and a minor axis of length 2b = 10.
Start by finding the length of the semi-major axis (a) and semi-minor axis (b). In this equation, a = 7 and b = 5. Then, plot the center (0,0). Since this is a horizontal ellipse, plot points (+a, 0) and (-a, 0) and (+b, 0) and (-b, 0) on the x-axis. Connect these points smoothly to form the ellipse.