General Parabola (1 Viewer)

[Aysce]

Okay I'm new to this topic and know what to do for this question, but I don't understand where I went wrong. Trust me I've looked for what I did wrong and couldn't find anything. Anyways:

Find the equation of the parabola with Vertex (1,0), and Focus (1,4).

Okay so my working is :

To find the focal length, it is the distance between the vertex and focus, which is 4, therefore a=4.

So wouldn't the equation then be, (x-1)^2 = 16(y-0) ?

The answer is x^2 - 2x - 12y + 1 = 0

 

[jnney]

I got the same answer as you.

 

[jnney]

the suggested answer is wrong anyways, because if you change it into the form of x^=4ay

by completing the square:

x^2-2x+(-1)^2-12y+1-1=0

(x-1)^2-12y=0

it becomes (x-1)^2 = 12y

the focal length is 4 as you said, not 3.

 

[Alkanes]

is this from fitzpatrick?

 

[Aysce]

Maths in focus :L I don't know about this question, but I did another question which has the same style and I still got a wrong answer. So it could be me? I don't think the answers could be wrong two times in a row oo

 

[jnney]

I've done all the questions in maths in focus lmao.

what was the other question?

 

[Drongoski]

I think (x-1)² = 16y is correct.

 

[jnney]

Well there you go, problem solved.

 

[Aysce]

hahs the other one was Find the equation of the parabola that has vertex (1,1) and focus (1,8). The answer I got was (x-1)^2 = 28(y-1), while the actual answer was x^2 - 2x - 28y+29 = 0

 

[jnney]

hahs the other one was Find the equation of the parabola that has vertex (1,1) and focus (1,8). The answer I got was (x-1)^2 = 28(y-1), while the actual answer was x^2 - 2x - 28y+29 = 0

Your answer is correct, but the suggested answer is also the same if you expand it.

 

[Drongoski]

hahs the other one was Find the equation of the parabola that has vertex (1,1) and focus (1,8). The answer I got was (x-1)^2 = 28(y-1), while the actual answer was x^2 - 2x - 28y+29 = 0

same thing!

 

[Aysce]

Oh wait that was my bad, got 29 from 28 x 1 ....

 

[SpiralFlex]

Oh wait that was my bad, got 29 from 28 x 1 ....

Make sure with these questions you put it in the form unless stated otherwise so that the vertex, directrix, focus, latus rectum length can be easily read.