The equation of a parabola with vertex at (0, 0) and directrix y = -3 is?
Practice Questions
1 question
Q1
The equation of a parabola with vertex at (0, 0) and directrix y = -3 is?
x^2 = -12y
y^2 = -12x
x^2 = 12y
y^2 = 12x
The distance from the vertex to the directrix is 3, so the equation is x^2 = -12y.
Questions & Step-by-step Solutions
1 item
Q
Q: The equation of a parabola with vertex at (0, 0) and directrix y = -3 is?
Solution: The distance from the vertex to the directrix is 3, so the equation is x^2 = -12y.
Steps: 7
Step 1: Identify the vertex of the parabola, which is given as (0, 0).
Step 2: Identify the directrix, which is given as y = -3.
Step 3: Calculate the distance from the vertex to the directrix. The vertex is at y = 0 and the directrix is at y = -3, so the distance is 0 - (-3) = 3.
Step 4: Since the directrix is below the vertex, the parabola opens downwards.
Step 5: Use the formula for the equation of a parabola that opens downwards: x^2 = -4py, where p is the distance from the vertex to the directrix.
Step 6: Substitute p = 3 into the formula: x^2 = -4(3)y.
