Directrix and focus of a parabola worksheet pdf

Parabola worksheet identify the vertex, focus, axis of symmetry, and directrix of each. Precalculus parabolas hw worksheet name day 1 monday. Equation focus directrix axis of symmetry behavior y. Finding the focus of a parabola given its equation. This activity allows me to assess what students are understanding with the equations. Standard form x h 2 4py k y k 2 4px h p 0 parabola opens up p 0 parabola opens right p 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. Parabolas and conic sections with videos, worksheets. Focus and directrix of a parabola notes example three. Sketch a graph the following parabolas label the vertex, focus, and directrix. This is by far the best way to solve for the directrix, focus and vertex. Find the focus and the directrix of a parabola precalculus. Graph, identify the 5 characteristics, and write the equation. Writing the equation of a parabola given the focus and. This worksheet is designed to help students with the topic of finding the focus and directrix of a parabola when given its equation.

The points on the parabola above and below the focus are 3, 6 and the graph is sketched in figure 9. Writing equations of parabolas in standard form college. 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. Following each math tutorial there are interactive questions or an optional printable worksheet which tests. 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. As stated before, the vertex is halfway between the directrix and the focus.

Weve already calculated the y values of the vertex 5. Given the vertex of a parabola is located at 2,2 and has a directrix of y 4, find the location of the focus. A 6 question worksheet continuation of notes is included. 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. Derive the equation of a parabola given a focus and directrix. Given its focus and directrix, write the equation for a parabola in standard form. To learn the relationship between the focus, directrix, vertex, and axis of a parabola and the equation of the parabola. Displaying all worksheets related to parabola axis of symmetry.

Z g amvaedbec 7w7intwhn binngf2ifnhi rtyed da hllg2e 3byr va s 12g. Following each math tutorial there are interactive questions or an optional printable worksheet which tests the understanding of key. I want students to notice that only one variable is squared for a parabola and the equation is not solved for a constant. Writing the equation of a parabola given the focus and directrix. The last problem requires the students to complete the square in order. How to find vertex, focus and directrix of a parabola equation. The focus lies on the axis of symmetry of the parabola. Students will learn the standard form of a parabola, and how to find the vertex, focus, and directrix for both vertical and horizontal parabolas. The worksheet gets gradually tougher as it continues.

Ffocus of a parabolaocus of a parabola big ideas learning. Given the vertex of a parabola is located at 2,1 and has a focus at 1,1, find the equation of the directrix. In the equation 2x 23x 4 0, the a value is greater than zero so the directrix is below the vertex. Use the information provided to write the standard form equation of each parabola. The receiver for the satellite is positions at the focus. Graph, identify the 6 characteristics, and write the equation of the parabola with vertex at 2, 3 and focus at 0, 3. As you can see from the diagrams, when the focus is above the directrix example 1, the. Eleventh grade lesson the parabola day 1 of 2 betterlesson. May 05, 2016 learn how to write the equation of a parabola given the focus and the directrix. Writing equations of parabolas in standard form college algebra. Start by putting the equation in th estandard form of. Students compare the standard equations and then predict how the general equation will look if it is representing a parabola.

How to find vertex, focus and directrix of a parabola. Displaying all worksheets related to focus and directrix. 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 exercises 914, put the equation into standard form and identify the vertex, focus, and directrix. Make sense of problems and persevere in solving them. Check point1 find the focus and directrix of the parabola given by then graph the parabola. The standard form of the equation of a parabola with vertex at h, k is as follows.

A parabola is the set of points equidistant from a fixed line called the directrix. 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. A 6 question worksheetcontinuation of notes is included. The directrix of the parabola is the horizontal line on the side of the vertex opposite of the focus. The red point in the pictures below is the focus of the parabola and the red line is the directrix. Use the information provided to write the vertex form equation of each parabola.

The image is reflected off one parabola to the other by the mirror of the parabolas. 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. The point is called the focus of the parabola and the line is called the directrix. When a signal hits the parabola it is projected to the focus. Because the focus is at 3, 0, substitute 3 for in the parabolas equation, replace with 3 in simplify. How to determine the vertex, focus and directrix of a. Precalculus parabolas hw worksheet name day 1 monday, march. Students have seen the standard equation and how it. Recall the standard form of the equation of a vertical parabola. Or if the parabola was down here, youd go straight up to find that distance. If you have the equation of a parabola in vertex form y a x.

I start out class with the student notes page, which has several examples of what todays lesson will be about. Because the focus is at 3, 0, substitute 3 for in the parabola s equation, replace with 3 in simplify. Find each of the requested components of a parabola. For x 2 4py, y p is the directrix for y 2 4py, x p is the directrix conic sections. Find the vertex, x and y intercepts and do a quick graph. A line perpendicular to the axis of symmetry used in the definition of a parabola. Vizual notes are an effective way to engage both the visual and logical sides of the brain. Finding equation of parabola with focus and directrix.

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. A parabola is the shape of the graph of a quadratic equation. Graph, identify the 5 characteristics, and write the equation of the parabola with vertex at 2, 3 and focus at 0, 3. The graph of an equation in the form y k ax hl2 is a parabola with vertex h, k and axis x h. For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix. 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. Parabolas, part 1 a quick way to roughly sketch a parabola. Students have seen the standard equation and how it is proved. 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. Learn how to write the equation of a parabola given the focus and the directrix. Eleventh grade lesson the parabola day 2 of 2 betterlesson.