Find the equation vertex (5, 2) Focus (3, 2)

Learn how to write the equation of a parabola given the vertex and the focus. A parabola is the shape of the graph of a quadratic equation. A parabola can open up or down (if x is squared) or open left or right (if y is squared). Recall that the focus and the vertex of a parabola are on the same line of symmetry.
When given the focus and the vertex of a parabola, recall that the focus of a parabola is inside the parabola. This enables us to identify the direction which the required parabola opens. We also need to identify the value of p, which is the distance between the vertex and the focus. p is negative when the parabola opens down or left and is positive when the parabola opens right or up.
Once we identify the direction and the value of p, we can use the equation of parabola given by (y - k)^2 = 4p(x - h) for parabolas that opens up or down and (x - h)^2 = 4p(y - k) for parabolas that opens left or right
#conicsections #parabolaconicsections

[@macjulian9495]

I think the graph is opening to the left so the p should be -2

[@brianmclogan]

correct! thank you just pinned your comment so no one else is confused

[@macjulian9495]

Brian McLogan But i hope my suggestion is correct

[@brianmclogan]

yes you are correct! my mistake

[@mekdeskassa5493]

Exactly 👌

[@joelfonseca8216]

what if the question is asking for the formula in terms of y=?

[@ormintukima9662]

Is certex the same with co vertex?

[@abhinaynayak4293]

Thanks for this solution I am gratfull for this sir

[@danaschannel4593]

What did you use in the formula for k and h ?? The vertex or focus!?

[@brianmclogan]

what do you mean?

[@jasbirsingh561]

Vertex......he/she is asking what does h,k symbolises......it mean hk is the vertex

[@kaitlynsturdivan7742]

I would love to be in your class.

[@brianmclogan]

you are, just online

[@jasbirsingh561]

So how was the information of focus of the parabola useful to us

[@brianmclogan]

It allowed up to find p and the (h,k) for the formula

[@jasbirsingh561]

Brian McLogan ok.... thanks

[@noni6513]

What if the vertex is (-5,2) and the focus is (3,2) need reply asap my teacher is really bad

[@azorgymcastro3652]

I think you should've use (y-k)=-4p(x-h) cause its opening towards the left side???

[@azorgymcastro3652]

I mean (y-k)^2=-4p(x-h)

[@brianmclogan]

I did use that form?

[@kevinesg]

should be -8 instead of 8 because it opens to the left

[@saivarada1242]

Why we take the formula (Y-k)² = 4p(x-h)..?? Why we didn't take the formula (Y-k)² = -4p(x-h)..???

[@brianmclogan]

because p is negative so that is what will make the equation negative, using your equation an using a negative p will then make the equation positive

[@skfeejan1235]

Whats the formula...? Can u tell

[@brianmclogan]

formulas are provided for conic sections

[@adilamjad9171]

Hy can you please solve this question find the equation of parabola whose vertex is (3,2) and the ends of focal chord are (5,6) and (5,-2) please solve this.

[@caratonceufrvr1610]

That shuold be -4p