Evaluate the parabola (y-2)^2=12(x-5)

Evaluate the parabola (y-2)^2=12(x-5)

Enter Parabola equation

Evaluate the vertical parabola

(y-2)2 = 12(x-5)

Open Direction

Since our squared variable is y, our parabola has a horizontal opening.

Determine the vertex (h,k):

Our standard for for this parabola is (y - k)2 = 4c(x - h)

Therefore, our vertex (h,k) = (5,2)

Determine focus:

From the right side of our standard form equation, we have 4c = 12

Divide each side by 4 to isolate c:

c = 3

The focus for a horizontal parabola is (h + c,k)

Substituting our values into this equation, we get:

Focus = (5 + 3,2)

Focus = (8,2)

Calculate the directrix:

The directrix equation for a horizontal parabola is x = c

Therefore, for c = 3, we have x = 3

How does the Parabolas Calculator work?

Free Parabolas Calculator - Determines the focus, directrix, and other related items for a parabola.
This calculator has 1 input.

What 5 formulas are used for the Parabolas Calculator?

standard horizontal parabola equation is y2 = 4cx
standard vertical parabola equation is x2 = 4cy
If the x coefficient is negative, then parabola opens left
If the x coefficient is positive, then parabola opens right

For more math formulas, check out our Formula Dossier

What 4 concepts are covered in the Parabolas Calculator?

directrixline in a parabola not through the focusfocusfixed point on the interior of a parabola used in the formal definition of the curveparabolaa plane curve which is approximately U-shapedparabolas

Example calculations for the Parabolas Calculator

Parabolas Calculator Video

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