Find b2 using c2 = a2 b2.

Tutorial Exercise Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: (0, +5); foci: (0, #3) Step 1 Recall that the major axis of an ellipse passes through the vertices and foci. From the coordinates of the vertices and foci, the major axis of the given ellipse is vertical vertical The vertices of the ellipse are given by (h, k + a). We are given that the center of the ellipse is at the origin and the vertices are at (0, +5). Therefore, h = 0, k = 0, and a = 5 5 Very nice!. Step 2 The foci of an ellipse in general form with vertical major axis are given by (h, k : c). We are given that the foci of the ellipse are (0, +3). Therefore, c = 3 Impressive work!. Step 3 Find b2 using c2 = a2 - b2. b2 = a2 - c2 =[ 2 - 32 =