Thursday

August 21, 2014

August 21, 2014

Posted by **sally** on Thursday, November 2, 2006 at 11:04am.

how would I derive the equation and focus, i've been trying to understand this for so long, I can't get it. Does this parabola have the equation (y-2)^2 = x and a focus of 1/4?? Is that correct??

I searched Google under the key words "

http://en.wikipedia.org/wiki/Parabola

http://www.tpub.com/math2/13.htm

http://colalg.math.csusb.edu/~devel/precalcdemo/conics/src/parabola.html

http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_conics_directrix.xml

http://mathworld.wolfram.com/Parabola.html

Use the <Find> command to locate keywords within these sites.

I hope this helps. Thanks for asking.

Formats to help you find the equation for a parabola:

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

Vertex = (h, k)

Focus = (h, k + p)

Directrix: y = k - p

You are given the vertex (0,2) and a point (1,1).

Let's try to find p using the vertex and the point you were given:

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

(1 - 0)^2 = 4p(1 - 2)

1 = 4p(-1)

1 = -4p

-1/4 = p

Let's try to find the equation now that we know p:

(x - 0)^2 = 4(-1/4)(y - 2)

x^2 = -1(y - 2)

x^2 = -y + 2

Set the equation equal to 0:

x^2 + y - 2 = 0 -->this is the equation for the parabola.

(You can check the point you were given by substituting the values into the equation.)

Focus = (h, k + p)

Therefore: (0, 7/4) is the focus.

Directrix: y = k - p

Therefore: y = 9/4

In this case, the focus is below the directrix; therefore, the parabola opens downward and p is negative.

I hope this helps.

**Related Questions**

pre cal - What is the center of the conic whose equation is x^2 + 2y^2 - 6x + ...

algebra - 6. Find the equation of each parabola described below. a) parabola ...

math - write an equation for the parabola with focus (1,3) and vetex (0,3) See ...

Pre Cal - write the equations of the parabola, the directrix, and the axis of ...

MATH - a parabola passes via the points (1.5,1) and (3,-5). given that the ...

Algebra - Can someone tell me if I am right? I need to find the equation of a ...

Alg 2 (ASAP) - I have a parabola vertex (11,3) p is not given, focus pt is not ...

algebra problem - I need to find the equation of a parabola. I am not sure if ...

College Algebra - Find the standard form of the equation of the parabola with ...

College Algebra - Find the standard form of the equation of the parabola with ...