Find the length of the latus rectum of the parabola y^2 = 16x.
Practice Questions
1 question
Q1
Find the length of the latus rectum of the parabola y^2 = 16x.
4
8
16
2
The length of the latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 16, so p = 4. Therefore, the length of the latus rectum is 4 * 4 = 16.
Questions & Step-by-step Solutions
1 item
Q
Q: Find the length of the latus rectum of the parabola y^2 = 16x.
Solution: The length of the latus rectum of a parabola y^2 = 4px is given by 4p. Here, 4p = 16, so p = 4. Therefore, the length of the latus rectum is 4 * 4 = 16.
Steps: 6
Step 1: Identify the equation of the parabola. The given equation is y^2 = 16x.
Step 2: Compare the given equation with the standard form of a parabola, which is y^2 = 4px.
Step 3: From the standard form, identify that 4p = 16.
Step 4: Solve for p by dividing both sides of the equation by 4. So, p = 16 / 4 = 4.
Step 5: Use the formula for the length of the latus rectum, which is 4p.
Step 6: Substitute the value of p into the formula: Length of latus rectum = 4 * 4 = 16.
