The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis

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Question: The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is given by?

Options:

Correct Answer: y^2/a^2 + x^2/b^2 = 1

Solution:

The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is y^2/a^2 + x^2/b^2 = 1.

The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is given by?

The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is given by?

Step 1: Understand that an ellipse is a shape that looks like a stretched circle.
Step 2: Know that the foci of the ellipse are points that help define its shape. In this case, the foci are at (0, ±c), which means they are located on the y-axis.
Step 3: Recognize that the major axis is the longest diameter of the ellipse. Since the major axis is along the y-axis, the ellipse is taller than it is wide.
Step 4: The standard form of the equation for an ellipse with a vertical major axis is y^2/a^2 + x^2/b^2 = 1.
Step 5: In this equation, 'a' represents the distance from the center to the top or bottom of the ellipse (along the y-axis), and 'b' represents the distance from the center to the sides of the ellipse (along the x-axis).
Step 6: The values of 'a' and 'b' are related to 'c' (the distance from the center to the foci) by the equation c^2 = a^2 - b^2.

Ellipse Properties – Understanding the standard form of the equation of an ellipse, including the orientation based on the position of foci and the major axis.
Coordinate Geometry – Applying knowledge of coordinates to identify the foci and axes of the ellipse.