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the parabola having its focus at (3,2) and directrix along the y-axis has its vertex at:

the parabola having its focus at (3,2) and directrix along the y-axis has its vertex at:

Grade:11

2 Answers

Shahid
74 Points
4 years ago
Let the Equation of the Parabola be (y-k)2 = 4a(x-h) 
It’s vertex is (h.k)
The Equation of Directrix for this parabola is (according to the equation) is x+a = h               ------{1}
It’s Focus is (a+h,k) = (3,2)
Thus a+h = 3                                                                        ---------{2}
        k = 2 
 
Directrix along the y-axis … Therefore Equation of Directrix is x=0                         -------------{3}
 
Now , {1} and {3}  represents the same line... 
Therefore , a = h 
Substituting this in {2}  , we get 
2h = 3 
h = 3/2
 
 
Now... Vertex = (h.k) = (3/2 ,2 )
RAVI KUMAR
21 Points
3 years ago
(y-k)^2=4p(x-h)
Since,the vertex and focus are3 unit apart, we have p=3, and since the vertix is at(h,k)=1,2, we obtain
(y-2)^2=12(x-1) 

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