Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.Find the standard form of the equation of the parabola with a focus at (7, 0) and a directrix at x = -7.

Question

anonymous · Answer

@mathstudent55 @Compassionate

compassionate · Answer

Sorry, not good with upper maths!

anonymous · Answer

Thanks though! @Compassionate

anonymous · Answer

@Preetha

anonymous · Answer

@YanaSidlinskiy @dan815 @just_one_last_goodbye @sleepyjess

sleepyjess · Answer

Sorry I learned this last year and do not remember anything about it.

anonymous · Answer

I have an example but I don't understand it either

anonymous · Answer

Example
We can also write the equation of a parabola if we are given information about it. For example, let's write the equation of a parabola whose focus is at (-4, 0) and whose directrix is the line x = 8

We begin by sketching the given information and noting that our parabola has a horizontal axis and must open to the left. It therefore has the form

(y - k )2 = 4p(x - h), p ≠ 0 

We must find the values of  h, k, and p.

Since the distance from focus to directrix is 2p ( the distance from each to the vertex is p), 2p = 12 and |p| = 6. For a left-opening parabola, p = -6. This puts the vertex at the point (2, 0) with h = 2, and k = 0. The equation is therefore (y – 0)2 = -24 ( x – 2).

This can be written as either y2 = –24 (x – 2) 

or
x equals negative one divided by twenty four y squared plus two.

anonymous · Answer

attachment

anonymous · Answer

@sleepyjess

sleepyjess · Answer

I am so sorry, but I really don't get it either. $\huge\ddot\frown$

yanasidlinskiy · Answer

Sure, I can help! That's why we're here for!:) 
the focus is at (7, 0), the directrix in a parabola is equidistant from the vertex to the focus
that is, the same distance from the vertex to the focus, is the distance from the vertex to the directrix

so the directrix is at x= -7

notice the focus is to the right side of the origin
and the directrix is to the left side

that means the parabola is opening horizontally

half-way between the directrix and the focus is, of course the vertex
between x = 7 and x =-7, the half-way is the origin, (0, 0)

so the center is at (0, 0)

so the parabola looks like this:|dw:1417983618229:dw|