Directrix and focus of a parabola worksheet pdf

Find the focus and the directrix of a parabola precalculus. A parabola is the set of all points that have a greater y value than a single point, called the focus of the parabola, and a lesser x value than a single point, called the directrix of the parabola. A parabola is the collection of all points in the plane that are the same distance from a fixed point, called the focus f, as they are from a fixed line, called the directrix d. Equation focus directrix axis of symmetry behavior y. When a signal hits the parabola it is projected to the focus. Students will learn the standard form of a parabola, and how to find the vertex, focus, and directrix for both vertical and horizontal parabolas. A parabola is a locus of points equidistant from both 1 a single point, called the focus of the parabola, and 2 a line, called the directrix of the parabola. Finding the focus of a parabola given its equation. This activity allows me to assess what students are understanding with the equations. Ffocus of a parabolaocus of a parabola big ideas learning.

Z g amvaedbec 7w7intwhn binngf2ifnhi rtyed da hllg2e 3byr va s 12g. A 6 question worksheet continuation of notes is included. For x 2 4py, y p is the directrix for y 2 4py, x p is the directrix conic sections. Students have seen the standard equation and how it. A parabola is the shape of the graph of a quadratic equation. Displaying all worksheets related to parabola axis of symmetry. Nothing about directrix and focus in this video look in part 2. Check point1 find the focus and directrix of the parabola given by then graph the parabola. Ffocus of a parabolaocus of a parabola a parabola can be defi ned as the set of all points x, y in a plane that are equidistant from a fi xed point called the focus and a fi xed line called the directrix. How to find vertex, focus and directrix of a parabola. Students compare the standard equations and then predict how the general equation will look if it is representing a parabola. Because the focus is at 3, 0, substitute 3 for in the parabolas equation, replace with 3 in simplify. Precalculus parabolas hw worksheet name day 1 monday.

Precalculus parabolas hw worksheet name day 1 monday, march. In the equation 2x 23x 4 0, the a value is greater than zero so the directrix is below the vertex. Focus and directrix of parabola explained with pictures. Finding equation of parabola with focus and directrix. Because the focus is at 3, 0, substitute 3 for in the parabola s equation, replace with 3 in simplify. Focus and directrix of a parabola notes example three. Recall the standard form of the equation of a vertical parabola. Writing equations of parabolas in standard form college algebra.

Weve already calculated the y values of the vertex 5. Graph the given characteristics and then finish the graph of the parabola. This worksheet is designed to help students with the topic of finding the focus and directrix of a parabola when given its equation. Learn how to write the equation of a parabola given the focus and the directrix.

The points on the parabola above and below the focus are 3, 6 and the graph is sketched in figure 9. I want students to notice that only one variable is squared for a parabola and the equation is not solved for a constant. In exercises 914, put the equation into standard form and identify the vertex, focus, and directrix. The graph of an equation in the form y k ax hl2 is a parabola with vertex h, k and axis x h. Writing the equation of a parabola given the focus and directrix. The directrix of the parabola is the horizontal line on the side of the vertex opposite of the focus. Graph, identify the 5 characteristics, and write the equation of the parabola with vertex at 2, 3 and focus at 0, 3. Parabolas, part 1 a quick way to roughly sketch a parabola. The receiver for the satellite is positions at the focus.

Parabola worksheet identify the vertex, focus, axis of symmetry, and directrix of each. These are all, these are all right angles right over here. Or if the parabola was down here, youd go straight up to find that distance. Eleventh grade lesson the parabola day 1 of 2 betterlesson. Eleventh grade lesson the parabola day 2 of 2 betterlesson. How to determine the vertex, focus and directrix of a. Find each of the requested components of a parabola. This is by far the best way to solve for the directrix, focus and vertex. Derive the equation of a parabola given a focus and directrix.

Find the vertex, x and y intercepts and do a quick graph. Determine whether the axis of symmetry is the x or yaxis if the given coordinates of the focus have the form latex\leftp,0\rightlatex, then the axis of symmetry is the xaxis. In the mirage the hologram is at the focus of the bottom parabola and the actual pig is at the focus of the top parabola. Graph, identify the 5 characteristics, and write the equation. And every parabola is going to have a focus and a directrix, because every parabola is the set of all points that are equidistant to some focus and some directrix. Use the information provided to write the vertex form equation of each parabola. The worksheet gets gradually tougher as it continues. If you have the equation of a parabola in vertex form y a x. Parabolas and conic sections with videos, worksheets. Vizual notes are an effective way to engage both the visual and logical sides of the brain. Following each math tutorial there are interactive questions or an optional printable worksheet which tests. The red point in the pictures below is the focus of the parabola and the red line is the directrix.

The standard form of the equation of a parabola with vertex at h, k is as follows. Students have seen the standard equation and how it is proved. Graph, identify the 6 characteristics, and write the equation of the parabola with vertex at 2, 3 and focus at 0, 3. A line perpendicular to the axis of symmetry used in the definition of a parabola. How to find vertex, focus and directrix of a parabola equation. The parabola opens to the left with vertex 2, 1, focus, 1, and directrix x parabola with vertex h, k and vertical axis x h2 4py k p 0. May 05, 2016 learn how to write the equation of a parabola given the focus and the directrix. Following each math tutorial there are interactive questions or an optional printable worksheet which tests the understanding of key. The last problem requires the students to complete the square in order. Start by putting the equation in th estandard form of.

A parabola is the set of points equidistant from a fixed line called the directrix. Writing the equation of a parabola given the focus and. Given its focus and directrix, write the equation for a parabola in standard form. Use the information provided to write the standard form equation of each parabola. As stated before, the vertex is halfway between the directrix and the focus. Displaying all worksheets related to focus and directrix. The point is called the focus of the parabola and the line is called the directrix. Given the vertex of a parabola is located at 2,2 and has a directrix of y 4, find the location of the focus. To learn the relationship between the focus, directrix, vertex, and axis of a parabola and the equation of the parabola. As you can see from the diagrams, when the focus is above the directrix example 1, the. The formal definition of a parabola is the set of all points that are the same distance from a single point of the parabola, called the focus, and a line of the parabola, called the directrix. The focus lies on the axis of symmetry of the parabola.