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What is the focus of the parabola given by the equation  (y-3)^2=8(x-5)?

 Jul 9, 2014

Best Answer 

 #2
avatar+130514 
+5

  (y-3)^2=8(x-5)

Let's see how Melody arrived at this......

Writing this in a slightly different form, we have

 (y-3)^2=4p(x-5)   where "p" is the distance (horizontal, in this case) between the x coordinate of the vertex and the x coordinate of the focal point.

So...we have.....

4p = 8   ..... and solving for "p"  we have

p = 2    ........i.e., the focal point is 2 units to the "right" from the vertex......thus......

The vertex is (5,3) and the focus is (7,3)......just as Melody found !!!!

For a "sideways" parabola that opens to the right, we add "p" to the x coordinate of the vertex. For one that opens to the left, we subtract "p" from the x coordinate of the vertex.

 

  

 Jul 9, 2014
 #1
avatar+118723 
+5

mmm let's think about that.

The vertex is (5,3)

It is a (pos) sideways parabola 8=4*2 so the focal length is 2.

So the focus must be y=3 x=5+2     

focus (7,3)

that sounds right to me.  

 Jul 9, 2014
 #2
avatar+130514 
+5
Best Answer

  (y-3)^2=8(x-5)

Let's see how Melody arrived at this......

Writing this in a slightly different form, we have

 (y-3)^2=4p(x-5)   where "p" is the distance (horizontal, in this case) between the x coordinate of the vertex and the x coordinate of the focal point.

So...we have.....

4p = 8   ..... and solving for "p"  we have

p = 2    ........i.e., the focal point is 2 units to the "right" from the vertex......thus......

The vertex is (5,3) and the focus is (7,3)......just as Melody found !!!!

For a "sideways" parabola that opens to the right, we add "p" to the x coordinate of the vertex. For one that opens to the left, we subtract "p" from the x coordinate of the vertex.

 

  

CPhill Jul 9, 2014
 #3
avatar+118723 
0

thanks chris,

You need to skech a graph of it then it should be clear.

 Jul 9, 2014
 #4
avatar+130514 
0

I would, except I'm at a public library, and it's hard to upload/download stuff here.....maybe I'll do it later....!!!!

 

  

 Jul 9, 2014
 #5
avatar+3454 
0

Your at a library? Why are you at a-

Nevermind, I won't ask.

 Jul 9, 2014
 #6
avatar+118723 
0

I wasn't meaning you Chris.  I was meaning Ashton!

 Jul 10, 2014
 #7
avatar+394 
0

His computer is probably in for repair.  Maybe the lame questions he answers caused it to overheat. Computers seem to get tired of things and get burnt out.

I hope CPhill doesn’t get burnt out!

 Jul 10, 2014
 #8
avatar+118723 
0

If Chris were here he would have some witty come back for you but he is not here so ALL 

you get is "yes yes, very funny 7up!"

I suppose you want some points now?

 Jul 10, 2014
 #9
avatar+394 
0

It’s not funny enough for points.

Only the CORRECT answers to questions should get points.

Maybe only REALLY funny posts or REALLY cool posts should get a point.

The points on here are already so inflated they almost aren’t worth anything!

7up

 Jul 10, 2014
 #10
avatar+118723 
0

I think that you are right sevenUP.

The points should be given for high achievement.  They should not reflect mediocrity!

 Jul 10, 2014
 #11
avatar+394 
0

What? No points for my brilliant post? LOL

 Jul 10, 2014
 #12
avatar+118723 
0

Yes, at your sensible request, no points!

 Jul 12, 2014

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