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The focus of a parabola is  (−3,−5) . The directrix of the parabola is y=2

.

What is the equation of the parabola?

y=−1/28(x−3/2)^2−3

y=−1/28(x+3)^2+3/2

y=−1/14(x−3/2)^2+3

y=−1/14(x+3)^2−3/2

I am thinking it is D

Feb 6, 2019

#1
+3

The y coordinate of the focus is below the directrix.....thus....this turns downward

Find the vertex =  ( -3 , (-5 + 2)/2 ) =  (-3, -3/2)

Find p  ..... l -3/2 -  - 5 l  = l  5 - 3/2 l  = [ 10/2 - 3/2 l  =  7/2

So.....we have the form

-4p(y - k) = (x - h)^2

-4(7/2)(y - -3/2) = (x - - 3)^2      simplify

-14 ( y + 3/2) = (x + 3)^2             mutiply both sides by -1/14

y + 3/2 = -(1/14) ( x + 3)^2        subtract 3/2 from both sides

y =  -(1/14)(x + 3)^2 - 3/2

Looks like you are correct, jenny  !!!   Feb 6, 2019
edited by CPhill  Feb 6, 2019
#3
+1

From your explantation in the other question it really helped ! Thank you

jjennylove  Feb 6, 2019
#4
+2

OK....   CPhill  Feb 6, 2019
#5
+1

The one where you went over each step more in depth

jjennylove  Feb 6, 2019
#6
0

The one above is the steps I took as well thank you .

jjennylove  Feb 6, 2019
#2
+1

this one if you can also

The directrix of a parabola is y=−8 . The focus of the parabola is  (−2,−6)

.

What is the equation of the parabola?

y=−1/8(x+2)^2+7

y=1/4(x+2)^2−7

y=1/8(x−2)^2−7

y=−1/4(x−2)^2−7

i think it is option 2

Feb 6, 2019
#7
+2

Second one.....the dirctrix is below the focus....this turns upward

Vertex    ( -2 ,  (-6 - 8)/2 )  = (-6, -14/2)  = (-2, -7)    = (h, k)

"p" =  l -7 - - 6 l =   l -1 l   =   1

We have the form

4p(y - h ) =  (x - k)^2

4(1) ( y - - 7) =  ( x - - 2)^2

4 (y + 7) = ( x + 2)^2            multiply both sides by 1/4

y + 7 =  (1/4) ( x + 2)^2       subtract 7 from both sides

y =  (1/4)(x + 2)^2 - 7

Looks good  !!!   CPhill  Feb 6, 2019
#8
+1

I have this one and jsut 1  more if can double check for me I understand if you cant

The directrix of a parabola is the line y=7 . The focus of the parabola is (2,3)

.

What is the equation of the parabola?

y=−1/8(x−2)^2−5

y=−1/8(x−2)^2+5

y=1/8(x−2)^2+5

y=1/8(x−2)^2−5

i think it is option c

jjennylove  Feb 6, 2019
edited by jjennylove  Feb 6, 2019
#9
+2

The directrix of a parabola is the line y=7 . The focus of the parabola is (2,3)

Remember jenny....if the y coordinate of the focus is less than the directrix....the parabola turns downward

Vertex     ( 2,  (3+7)/2)  = (2, 10/2) = ( 2, 5)  = (h, k)

"p"  =  l  5 - 3 l = l 2 l = 2

We have the form

-4p(y - k) = (x - h)^2

-4(2) ( y - 5) = ( x - 2)^2

-8 ( y - 5) = ( x - 2)^2        divide both sides by -1/8

y - 5 =  (-1/8)( x - 2)^2

y = -(1/8) ( x - 2)^2 + 5   CPhill  Feb 6, 2019
#10
+1

If you can check this last one since I am worried because I did not get that other one correct

The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3

.

What is the equation of the parabola?

y=−1/2x^2−52

y=1/2x^2−52

y=1/4x^2−2

y=−1/4x^2+2

i think it would be option B

jjennylove  Feb 6, 2019
#11
+1

oh okay I see where I made my mistake, I have to watch out for whether it goes downward or upward

jjennylove  Feb 6, 2019
#12
+3

The focus of a parabola is (0,−2) . The directrix of the parabola is the line y=−3

The y coordinate of the focus is > the y value of the directrix....thus this opens upward

Vertex    ( 0, (-3 +   -2) /2 )   =   ( 0,  -5/2)   =  (h, k)

"p"  =   l  -5/2 - - 2 l  =  l  - 5/2 + 2 l  =   l -5/2 + 4/2 l  =  l -1/2  l = 1/2

The form is

4p ( y - k) = ( x - h)^2

4(1/2) ( y -  - 5/2) = (x - 0)^2

2(y + 5/2) = x^2        multiply both sides by  1/2

y + 5/2  =  (1/2)x^2

y = (1/2)x^2  - 5/2

Feb 6, 2019
#13
+1

THANK YOU!! This all helped so much jjennylove  Feb 6, 2019