+0  
 
0
124
1
avatar+181 

Question 1)

Question 2)

Johnnyboy  May 5, 2018
edited by Johnnyboy  May 5, 2018
 #1
avatar+88902 
+1

1.   16(x - 3)  =  (y - 1)^2 

 

The vertex of this parabola is at  ( 3, 1)

This parabola opens to the right

In the form    4p(x - 3)  = (y - k)^2......the focus is  ( 3 + p, 1)   

We can solve for p as  4p  =16  ⇒   p  = 4

So....the focus  is  ( 3 + 4, 1)   =  (7,1)

The dirctrix lies 4 units to the left of the vertex and is given by    x  = ( 3 - p )  =   (3  - 4 )   =    -1

Here's a graph :  https://www.desmos.com/calculator/iwubncnnan

 

2.  y  = -1/6 x^2 + 7x  - 80     we need to complete the square on  x

 

y  = (-1/6)  [ x^2- 42x + 480 ]     

 

Take 1/2 of 42  = 21....square it  = 441....add and subtract it within the brackets

 

y   =    (-1/6)  [x^2 - 42x + 441 + 480  - 441 ]     factor the frist three terms....simplify the rest

 

y  = (-1/6) [  (x - 21)^2  + 39 ]

 

y = (-1/6)(x - 21)^2  - 39/6

 

y  = (-1/6)(x - 21)^2  - 13/2       add 13/2 to both sides

 

(y + 13/2) =  (-1/6)(x - 21)^2        multiply through  by -6

 

-6(y + 13/2)  = (x - 21)^2

 

Because of the presence of a "-"   in front of the "6"......this parabola turns downward

The vertex is  ( 21, - 13/2)

The focus is  given by ( 21 , -13/2  + p )

And we can find  p as    .....  4p  = -6   ⇒  p  = -6/4  = -3/2

So....the  focus  is  (21, -13/2 - 3/2)   = ( 21 , -16/2)  = (21, -8)

The directerix is given as    y  = (-13/2 - p)   = ( -13/2 - (-3/2) )   = ( -13/2 + 3/2)  = -10/2  = -5

Here's a graph :  https://www.desmos.com/calculator/g9zfw92yos

 

 

cool cool cool

CPhill  May 5, 2018
edited by CPhill  May 5, 2018

33 Online Users

avatar
avatar
avatar
avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.