SOLUTION: a. Find the co-ordinates of the vertex and the focus of the parabola x^2=4(x+y). Find the foci and vertices of the hyperbola 9 x^2 - y^2 - 36x +8y - 5 = 0 .

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: a. Find the co-ordinates of the vertex and the focus of the parabola x^2=4(x+y). Find the foci and vertices of the hyperbola 9 x^2 - y^2 - 36x +8y - 5 = 0 .      Log On


   

Question 440689: a. Find the co-ordinates of the vertex and the
focus of the parabola x^2=4(x+y).
Find the foci and vertices of the hyperbola
9 x^2 - y^2 - 36x +8y - 5 = 0 .
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi



a. Find the co-ordinates of the vertex and the focus of the parabola 

 x2=4(x+y)

 x^2 - 4x = 4y

 (x-2)^2 - 4 = 4y  OR (x-2)^2 = 4(y+1)

Using the vertex form of a parabola, y=a%28x-h%29%5E2+%2Bk where(h,k) is the vertex

 1/4(x-2)^2 - 1 = y   Vertex (2,-1)

 The standard form is %28x+-h%29%5E2+=+4p%28y+-k%29, where  the focus is (h,k + p) 

                        (x-2)^2 = 4(y+1)  4p = 4 , p = 1 focus(2,0)