Find the equation of the following eclipse.
Focus (0,+- 2), length of the major axis is 8.
Focus (0,+- 2), length of the major axis is 8.
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x^2/12 + y^2/16=1.
The length of the major axis is 8, so you know that your vertices are (0, 4) and (0, -4) because your foci are on the y-axis, and that makes the y-axis the major axis. You can assign 4 to be the value of a, and 2 to be the value of c, so you need to solve for b. c^2=a^2 - b^2, and you can substitute values to get 4= 16-b^2. From there, you can see that b is the square root of 12, or two square roots of 3. However, since the standard form of an ellipse has b^2 under either x^2 or y^2, you can just leave it as 12 in the equation in standard form.
The x-axis is the minor axis, so 12 goes under x^2. The y-axis is the major axis, so 4^2, or 16, goes under y^2. Your final answer is x^2/12 + y^2/16=1.
The length of the major axis is 8, so you know that your vertices are (0, 4) and (0, -4) because your foci are on the y-axis, and that makes the y-axis the major axis. You can assign 4 to be the value of a, and 2 to be the value of c, so you need to solve for b. c^2=a^2 - b^2, and you can substitute values to get 4= 16-b^2. From there, you can see that b is the square root of 12, or two square roots of 3. However, since the standard form of an ellipse has b^2 under either x^2 or y^2, you can just leave it as 12 in the equation in standard form.
The x-axis is the minor axis, so 12 goes under x^2. The y-axis is the major axis, so 4^2, or 16, goes under y^2. Your final answer is x^2/12 + y^2/16=1.