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

Let (x0,y0) be any point on the parabola. Find the distance between (x0,y0) and the focus. Then find the distance between (x0,y0) and directrix. Equate these two distance equations and the simplified equation in x0 and y0 is equation of the parabola.

How do you find the focus of a parabola given the 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+14a).

WHAT IS A in Parabola equation?

For graphing, the leading coefficient “a” indicates how “fat” or how “skinny” the parabola will be. Parabolas always have a lowest point (or a highest point, if the parabola is upside-down). This point, where the parabola changes direction, is called the “vertex”.

How do you write an equation for a parabola?

This straight line outside the parabola is called the directrix. For parabolas that open either up or down, the standard form equation is (x – h)^2 = 4p(y – k). For parabolas that open sideways, the standard form equation is (y – k)^2 = 4p(x – h). The vertex or tip of our parabola is given by the point (h, k).

How do you find the equation of a parabola given two points?

Using the vertex form of a parabola f(x) = a(x – h)² + k where (h,k) is the vertex of the parabola.The axis of symmetry is x = 0 so h also equals 0.a = 1.Substituting the a value into the first equation of the linear system:k = 3.f(1) = 4 = (1 – 0)² + 3 = 1 + 3.f(2) = 7 = (2 – 0)² + 3 = 4 + 3.

What is the focus and directrix of a parabola?

What are the focus and directrix of a parabola? Parabolas are commonly known as the graphs of quadratic functions. They can also be viewed as the set of all points whose distance from a certain point (the focus) is equal to their distance from a certain line (the directrix).

How do you solve an equation on a graphing calculator?

TI-84 Plus Graphing Calculator For Dummies Press [GRAPH][ZOOM][7] to select the Eqns/Coords tool from the MEAS menu. Use the arrow keys to move the cursor to the object whose equation or coordinates you want to find and press [ENTER]. The equation or coordinates appear at the location of the cursor.

What is a parabola in real life?

This reflective property is the basis of many practical uses of parabolas. The parabola has many important applications, from a parabolic antenna or parabolic microphone to automobile headlight reflectors and the design of ballistic missiles. They are frequently used in physics, engineering, and many other areas.