What is the equation of the parabola whose focus is at 0 3 )?
Table of Contents
- 1 What is the equation of the parabola whose focus is at 0 3 )?
- 2 What is the standard form of the equation of the parabola with vertex at 0 0 and focus 0 5 )?
- 3 How do you find the vertex focus and directrix of a parabola?
- 4 Which is the equation of a parabola with focus 0 5?
- 5 How do you find the vertex of a parabola?
- 6 How do you find the vertex of a graph?
What is the equation of the parabola whose focus is at 0 3 )?
Vertex of the parabola is (0,0) and its focus is (0,-3). These informations indicate that the parabola is open downwards. So its equation must be x^2 = -4at.
What is the equation of a parabola with vertex 0 0 and a focus at 2 0?
The equation of a parabola with vertex (0, 0) and focus (0, 2) is y = (1/8)x2.
What is the standard form of the equation of the parabola with vertex at 0 0 and focus 0 5 )?
Explanation: Focus is at (5,0) and vertex is at (0,0) . the equation of parabola is y2=4ax , a=5 is the focal distance (the distance from vertex to focus).
What is the equation of a parabola?
Parabola Equation The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. Directrix: The line drawn parallel to the y-axis and passing through the point (-a, 0) is the directrix of the parabola. The directrix is perpendicular to the axis of the parabola.
How do you find the vertex focus and directrix of a parabola?
The standard form is (x – h)2 = 4p (y – k), where the focus is (h, k + p) and the directrix is y = k – p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y – k)2 = 4p (x – h), where the focus is (h + p, k) and the directrix is x = h – p.
Which of the following is an equation for a parabola with focus a 0?
A General Note: Standard Forms of Parabolas with Vertex (0, 0)
| Axis of Symmetry | Equation | Focus |
|---|---|---|
| x-axis | y2=4px | (p, 0) |
| y-axis | x2=4py | (0, p) |
Which is the equation of a parabola with focus 0 5?
Summary: The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is y = x2 /20.
Which is the equation of a parabola with focus 0 5 and Directrix Y?
y = x2 /20
Summary: The equation of the parabola whose focus is at (0, 5) and directrix at y = -5 is y = x2 /20.
How do you find the vertex of a parabola?
Find the Parabola with Focus (0,5) and Directrix y=-5 (0,5) , y=-5 Since the directrix is vertical, use the equation of a parabola that opens up or down. Find the vertex. Tap for more steps… The vertex ( h, k) ( h, k) is halfway between the directrix and focus.
How do you find the distance between the focus and vertex?
The distance from the focus to the vertex and from the vertex to the directrix is | p | | p |. Subtract the y y coordinate of the vertex from the y y coordinate of the focus to find p p. Subtract 0 0 from 3 3. Substitute in the known values for the variables into the equation (x−h)2 = 4p(y−k) ( x – h) 2 = 4 p ( y – k).
How do you find the vertex of a graph?
Find the vertex. Tap for more steps… The vertex ( h, k) ( h, k) is halfway between the directrix and focus. Find the y y coordinate of the vertex using the formula y = y coordinate of focus + directrix 2 y = y coordinate of focus + directrix 2. The x x coordinate will be the same as the x x coordinate of the focus.