locus and parabola (1 Viewer)

[swifty13]

Can anyone please help me with this question?
The latus rectum of a parabola has end points (2,3) and (6,3). Find two possible equations for the parabola. I think it's to do with simulataneous equations but I don't know where to start.

 

[harrowed2]

Always draw a pretty diagram.




We can see there is clearly two possible cases, concave up and concave down.


Remember our general equation,



So what do we know about this latus rectum? We know it's 4 times to focal length!

The latus rectum is 4 units, so that means the focal length is 1 unit.

So,




What else do we know? Ah, it passes through the points,
and






So,













RAWR, we have two equations now,

These are the equations of parabolas with the same vertex, which they should not.

The latus rectum passes through the focus of each parabola , which will be the point (4,3).

Since the focal length is 1 unit, the vertices are:

(4,2) for the parabola that is concave up ---> equation is (x-4)^2=4(y-2)

and (4,4) for the parabola that is concave down -----> equation is (x-4)^2= -4(y-4)

 

[SpiralFlex]

Haha, didn't think about it when I posted. Thanks for correction.

 

[swifty13]

Thank you