What is the length of the latus rectum of the ellipse x^2/a^2 + y^2/b^2 = 1?
Practice Questions
1 question
Q1
What is the length of the latus rectum of the ellipse x^2/a^2 + y^2/b^2 = 1?
2b^2/a
2a^2/b
2a
2b
The length of the latus rectum of the ellipse is given by 2a^2/b.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the length of the latus rectum of the ellipse x^2/a^2 + y^2/b^2 = 1?
Solution: The length of the latus rectum of the ellipse is given by 2a^2/b.
Steps: 5
Step 1: Understand what an ellipse is. An ellipse is a shape that looks like a stretched circle.
Step 2: Know the standard form of an ellipse equation, which is x^2/a^2 + y^2/b^2 = 1. Here, 'a' and 'b' are constants that define the size and shape of the ellipse.
Step 3: Identify the latus rectum. The latus rectum is a line segment that passes through one of the foci of the ellipse and is perpendicular to the major axis.
Step 4: Learn the formula for the length of the latus rectum of an ellipse. The formula is 2a^2/b.
Step 5: Apply the formula. If you know the values of 'a' and 'b', you can plug them into the formula to find the length of the latus rectum.
