Table of Contents
What is the equation of the Directrix of the given parabola?
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 of the parabola having the vertex of the origin and Directrix?
(x – h)2 = 4p (y – k), where (h, k) is the vertex, the focus is (h, k + p), and the directrix is y = k – p.
What is Directrix parabola?
A parabola is set of all points in a plane which are an equal distance away from a given point and given line. The point is called the focus of the parabola, and the line is called the directrix . The directrix is perpendicular to the axis of symmetry of a parabola and does not touch the parabola.
How to find the equation of the directrix of a parabola?
1. You know the coordinates of vertex and focus Suppose you know the coordinates of vertex and focus of a parabola. In order to find the equation of its directrix, we will use two properties of the directrix to find its equation: The directrix is perpendicular to the axis of the parabola
How do you find the equation of a parabola with focus?
Therefore, the equation of the parabola with focus ( a, b) and directrix y = c is If the focus of a parabola is ( 2, 5) and the directrix is y = 3 , find the equation of the parabola. Let ( x 0, y 0) be any point on the parabola.
What is the slope of the axis of a parabola?
Then, the slope of the axis is, by the formula for slope of a straight line, Since the slope of the axis of the parabola is zero, this means that the axis of the parabola is parallel to the x-axis (all lines having slope zero are parallel to the x-axis).
How do you find the intercept of a parabola?
Sometimes you want to know where the parabola intercepts the x -axis. To get an equation with this intercept information in it already, use the standard form equation with ‘a’, ‘b’, and ‘c’. Then, factor out the ‘a’ to get y = a ( x ^2 + b x /a + c/a). Then use the quadratic equation to find the two roots p and q.