+1995 The focus of a parabola is (−3,−5) . The directrix of the parabola is y=2
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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
+129852 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 !!!
+1995 From your explantation in the other question it really helped ! Thank you
+1995 this one if you can also
The directrix of a parabola is y=−8 . The focus of the parabola is (−2,−6)
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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
+129852 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 !!!
+1995 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)
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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
+129852 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
+1995 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
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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
+1995 oh okay I see where I made my mistake, I have to watch out for whether it goes downward or upward
+129852 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
