How do you find the Directrix of a conic parabola?
The directrix is the line y = k – p. The axis is the line x = h. If p > 0, the parabola opens upward, and if p < 0, the parabola opens downward. If a parabola has a horizontal axis, the standard form of the equation of the parabola is this: (y – k)2 = 4p(x – h), where p≠ 0.
What is the equation of Directrix of parabola?
The axis of the parabola is y-axis. Equation of directrix is y = -a. i.e. y = -½ is the equation of directrix. Vertex of the parabola is (0,0).
What is the equation for parabola conic section?
STANDARD FORMS OF EQUATIONS OF CONIC SECTIONS:
| Circle | (x−h)2+(y−k)2=r2 | Center is (h,k) . Radius is r . |
|---|---|---|
| Parabola with vertical axis | (x−h)2=4p(y−k) , p≠0 | Vertex is (h,k) . Focus is (h,k+p) . Directrix is the line y=k−p . Axis is the line x=h |
What is Directrix in conic section?
The directrix of a conic section is the line which, together with the point known as the focus, serves to define a conic section as the locus of points whose distance from the focus is proportional to the horizontal distance from the directrix, with being the constant of proportionality.
How do you find the Directrix equation?
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.
What does 4p mean in parabola?
We need to take this number and set it equal to 4p. In this case, 4p is equal to the term in front of the y term (in parenthesis); so 4p = -6. This means that p = -3/2. Since this is an downward facing parabola, we need to have the focus inside of the curve, meaning the focus is below the vertex.
What are the coordinates of the focus and the equation of the Directrix?
What are the coordinates of its focus? The focus of a parabola is located at (0,-2). The directrix of the parabola is represented by y = 2.