3. 25x+4y² 100 Center: Vert CV: Foci:
Answer (1)
Answer:To find the center, vertices, and foci of the ellipse represented by the equation , we need to first put the equation in standard form for an ellipse. The standard form for an ellipse with a horizontal major axis is , where is the center of the ellipse, is the semi-major axis, and is the semi-minor axis. Given equation: Divide by 100 to simplify the equation: Simplify: Now, we have the equation in standard form: This gives us the center at , the semi-major axis , and the semi-minor axis . To find the vertices, we need to add and subtract the semi-major axis from the center: Vertices: and To find the foci, we use the formula for the distance from the center to the foci on the major axis: Foci: and Therefore, the center of the ellipse is at , the vertices are at and , and the foci are at and .
