The equation looks like this $\frac{ x^{2} }{16} + \frac{ y^{2} }{25} =1$ . In an ellipse, a is always the bigger value, so a^2 = 25. This bigger value also tells us which axis is the major one. Sine the bigger value a is under the y^2 of the equation, the major axis is the y-axis. This is a vertical ellipse. The center is always found within a set of parenthesis that exist with the x^2 and the y^2. Since there are no parenthesis with either, there is no side to side movement, nor is there any up or down movement. So the center doesn't move from the origin (0, 0). The vertex is also along the major axis, and if a^2 is 25, then a = 5, so the vertices go up 5 from the center and down 5 from the center. Vertices are (0, 5) and (0, -5). The foci follow the formula $c^{2}= a^{2}- b^{2}$ . c is the distance that the foci are from the center. $c^{2}=25-16$ and c = 3. The foci also lie on the major axis, so the coordinates for the foci are (0, 3) and (0, -3). There you go!

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2 years ago