The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis
Practice Questions
Q1
The equation of an ellipse with foci at (0, ±c) and major axis along the y-axis is given by?
x^2/a^2 + y^2/b^2 = 1
y^2/a^2 + x^2/b^2 = 1
x^2/b^2 + y^2/a^2 = 1
y^2/b^2 + x^2/a^2 = 1
Questions & Step-by-Step Solutions
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.
