What is the length of the latus rectum of the parabola y^2 = 4ax?
Practice Questions
1 question
Q1
What is the length of the latus rectum of the parabola y^2 = 4ax?
2a
4a
a
None of the above
The length of the latus rectum of the parabola y^2 = 4ax is 4a.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the length of the latus rectum of the parabola y^2 = 4ax?
Solution: The length of the latus rectum of the parabola y^2 = 4ax is 4a.
Steps: 6
Step 1: Understand what a parabola is. A parabola is a U-shaped curve that can open up, down, left, or right.
Step 2: Identify the standard form of the parabola given in the question, which is y^2 = 4ax. This means the parabola opens to the right.
Step 3: Recognize that 'a' in the equation y^2 = 4ax represents a specific distance related to the parabola.
Step 4: Learn about the latus rectum. The latus rectum is a line segment that is perpendicular to the axis of symmetry of the parabola and passes through the focus.
Step 5: For the parabola y^2 = 4ax, the length of the latus rectum is always equal to 4 times the value of 'a'.
Step 6: Therefore, if the equation is y^2 = 4ax, the length of the latus rectum is calculated as 4a.
