Maths Question (1 Viewer)

[Apex]

Find the coordinates of the focus of the parabola x^2=8(y-1)

I'm guessing you need to find the vertex but how do you do that? I read some -b/2a thing or something but didn't really understand it. Thanks

 

[letsdie45]

the parabola can be written in the form (x-h)^2 = 4a(y-k) where (h,k) is the vertex. So for x^2 = 8(y-1), the vertex is (0,1) and the focus is (0,3).

 

[TheStallion]

To find the vertex, find the axis of symmetry, using -b/2a like you already know. Axis of symmetry is an x value, so sub the axis of symmetry in the equation of the parabola to get the vertex.

No idea past that - we haven't done the focus/focal point/anything like that in 2U yet. Our class is behind like hell.

 

[- Alex -]

Find the coordinates of the focus of the parabola x^2=8(y-1)

I'm guessing you need to find the vertex but how do you do that? I read some -b/2a thing or something but didn't really understand it. Thanks

Use the general form of a parabola, (x-h)^2=4a(y-k) where (h,k) is the vertex, then the focus will be (h,k+a).

The vertex is (0,1) and since a = 8/4 = 2, the focus is (0,1+2) => (0,3)