For the parabola defined by the equation x^2 = 16y, what is the distance from th

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Question: For the parabola defined by the equation x^2 = 16y, what is the distance from the vertex to the focus?

Options:

Correct Answer: 4

Solution:

In the equation x^2 = 4py, we have 4p = 16, thus p = 4. The distance from the vertex to the focus is 4.

For the parabola defined by the equation x^2 = 16y, what is the distance from the vertex to the focus?

For the parabola defined by the equation x^2 = 16y, what is the distance from the vertex to the focus?

Step 1: Identify the given equation of the parabola, which is x^2 = 16y.
Step 2: Recognize that the standard form of a parabola that opens upwards is x^2 = 4py.
Step 3: Compare the given equation x^2 = 16y with the standard form x^2 = 4py.
Step 4: Notice that in the standard form, 4p corresponds to 16 in the given equation.
Step 5: Set up the equation 4p = 16 to find the value of p.
Step 6: Solve for p by dividing both sides of the equation by 4: p = 16 / 4.
Step 7: Calculate p, which gives p = 4.
Step 8: Understand that the distance from the vertex to the focus of the parabola is equal to p.
Step 9: Conclude that the distance from the vertex to the focus is 4.

Parabola Properties – Understanding the standard form of a parabola and the relationship between the coefficients and the distance to the focus.
Vertex and Focus – Identifying the vertex and focus of a parabola and calculating the distance between them.