Use the definition of a parabola and the distance

In summary, Pre-Calculus is a Math subject at a higher level than High School level, and some of the problems posted in Pre-Calculus are beyond what is covered in High School level Math.
  • #1
r-soy
172
1
Hi all

Use the definition of a parabola and the distance formula to find the equation of a parabola with

a ) directix x = -4 and focus (2,2 )
B ) directix x = 2 and focus (6,-4 )


How i solve like this queation please hle me the steps to solve that

thanks
 
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  • #2
Hi r-soy! :wink:
r-soy said:
Hi all

Use the definition of a parabola and the distance formula to find the equation of a parabola with

a ) directix x = -4 and focus (2,2 )
B ) directix x = 2 and focus (6,-4 )


How i solve like this queation please hle me the steps to solve that

thanks

First, write out the definition of a parabola, and the distance formula …

what are they? :smile:
 
  • #3
hhhh what is the formula ??
 
  • #4
r-soy said:
hhhh what is the formula ??

The "distance formula"?

I've no idea … you mentioned it. :confused:
 
  • #5
tiny-tim said:
The "distance formula"?

I've no idea … you mentioned it. :confused:
Aww, I'll bet you're just being coy, tiny-tim.:biggrin:
 
  • #6
Mark44 said:
Aww, I'll bet you're just being coy, tiny-tim.:biggrin:

uhh? oh, for a moment i thought you said "koi"! :blushing:

no, i really don't know which formula is being referred to (i'll guess it has something to do with the focus or the directrix)
 
  • #7
Here's the definition: A parabola is the set of all points equidistant from a fixed point (the focus) and a fixed line (the directrix).

The distance formula is the plain old distance formula we all know and love.
 
  • #8
Mark44 said:
The distance formula is the plain old distance formula we all know and love.

uhhh? do you mean Pythagoras? :confused:
 
  • #9
As I see it first the distance between the point (x,y) and (2,2) [The focus] can be expressed

[tex]\sqrt{(x-2)^2 + (y-2)^2} = 2+y[/tex]

which can be simplified to to find the expression for the parabol in case a..

Which gives us

[tex]y = \frac{x^2-4x+4}{8}[/tex] as the expression for the parabola in case a).

Susanne
 
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  • #10
Very good. However, I wonder if r-soy ever tried to do that, or if he even knows the definition of "parabola".
 
  • #11
HallsofIvy said:
Very good. However, I wonder if r-soy ever tried to do that, or if he even knows the definition of "parabola".

If not there is magically place out there called The Google and The Wikipedia which can give the definition of both the parabola and how and why to use the formula which I used in the above post.

But I say thanks for the compliment HallsoftIvy. Now I will sleep well knowing that the great HallsoftIvy gave me a thumbs up for my work for once :D

Have a nice day...

I consider Pre-Calculus to be High School level Math. But some of problems posted in Pre-Calculus are like Post Calculus and even post-Real Analysis here. Is it because what's Pre-Calculus in one country isn't the same all over?
 
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FAQ: Use the definition of a parabola and the distance

What is the definition of a parabola?

A parabola is a symmetrical curve formed by the intersection of a plane with a right circular cone when the plane is at an angle to the base of the cone.

How is a parabola different from other curves?

A parabola is unique in that it has one focus point and a directrix line that is perpendicular to the axis of symmetry. This means that all points on the parabola are equidistant from the focus and the directrix.

How can the distance formula be used to find points on a parabola?

The distance formula, which is the square root of the sum of the squared differences between the coordinates of two points, can be used to find the distance between any point on a parabola and its focus or directrix. This can help determine the coordinates of points on the parabola.

Can the distance between a point and a parabola be negative?

No, the distance between a point and a parabola is always positive. This is because distance is a measure of length and cannot be negative. If the point is outside of the parabola, the distance will be positive. If the point is inside the parabola, the distance will be zero.

How is the distance used to graph a parabola?

The distance formula can be used to graph a parabola by finding the distance between the focus and a point on the parabola for different values of x. These distances can then be plotted on a graph to form the curved shape of the parabola.

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