How do you find the focus of a parabola given its equation?

How do you find the focus of a parabola given its equation?

Finding the focus of a parabola given its equation If you have the equation of a parabola in vertex form y = a (x − h) 2 + k, then the vertex is at (h, k) and the focus is (h, k + 1 4 a).

What are the four possible orientations of the parabola?

The four such possible orientations of the parabola are explained in the table below: Equation Formulas y 2 = 4ax Focus = (a, 0); a > 0 Directrix: x = -a y 2 = -4ax Focus = (-a, 0); a < 0 Directrix: x = a x 2 = 4ay Focus = (0, a); a > 0 Directrix: y = -a x 2 = -4ay Focus = (0, -a); a < 0 Directrix: y = a

How do you find the axis of symmetry of a parabola?

Example 1: Find the coordinates of the focus, axis, the equation of the directrix and latus rectum of the parabola y 2 = 12x. to the right. Also, the axis of symmetry is along the positive x-axis. Focus of the parabola is (a, 0) = (3, 0). Equation of the directrix is x = -a, i.e. x = -3 or x + 3 = 0.

How do you find the coordinates of a point on a parabola?

For a parabola, the equation is y 2 = -4ax. Now, to represent the co-ordinates of a point on the parabola, the easiest form will be = at 2 and y = 2at as for any value of “t”, the coordinates (at 2, 2at) will always satisfy the parabola equation i.e. y 2 = 4ax. So,

What is a parabola in math?

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.

How do you know if a parabola faces up or down?

If the equation comes in the form of y = – (x – h)2+ k, the negative in front of the parenthesis tells us that the parabola is pointed downward (as illustrated in the picture below). If there is no negative sign in front, then the parabola faces upward. Example 2

How do you find the directrix of a parabola?

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.