Sketch the following 4x2 plus 25y2 equals 100?

Answer 1

4x2 + 25y2 = 100 (divide each element of both sides by 100)

x2/25 + y2/4 = 1 This is the equation of an ellipse of the form x2/a2 + y2/b2 = 1, whose center is at (0, 0), a = 5, b = 2, and so c = √(a2 - b2) = √19)

Since the major axis is horizontal and it lies on the x-axis, the vertices are 5 units to the left and 5 units to the right of the center (0, 0).

Vertices are (-5, 0) and (5, 0).

The minor axis is vertical and it lies on the y-axis, so the graph of the ellipse crosses the y-axis at the points (0, -2) and (0, 2), since b = 2)

The foci are √19 units to the left and √19 units to the right of the center (0, 0).

The foci are (-√19, 0) and (√19, 0).