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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

jjennylove 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 !!!

CPhill Feb 6, 2019

#3

#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

jjennylove 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

#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

CPhill Feb 6, 2019