How To Find The Equation Of A Parabola With Focus And Directrix

Then you substitute the parabolas equation into the rotation equations.

How to find the equation of a parabola with focus and directrix. The focus is located at h k p. Therefore the equation of the parabola with focus a b and directrix y c is. In this example the focus is at 4 3 so k p 3. Khan academy is a 501c3 nonprofit organization.

Y k x2. Theta is the angle through which you have rotated which is the angle between the origin and the directrix. Find the parabola with focus f 60 and directrix x6 60. Find the parabola with focus 04 and directrix y4 04 y4 since the directrix is vertical use the equation of a parabola that opens up or down.

Y ax2 bx c. X a 2 b 2 c 2 2 b c y. Focus directrix of a parabola from equation our mission is to provide a free world class education to anyone anywhere. Find the vertex.

There are two form of parabola equation standard form and vertex form. X6 since the directrix is horizontal use the equation of a parabola that opens left or right. The vertex of the parabola. A parabola is a curve where any point is at an equal distance from a fixed point called the focus and a fixed straight line called the directrix.

Y a x h2 k. Y y cos theta x sin theta x y is the coordinate of the new point after rotation. If the focus of a parabola is 2 5 and the directrix is y 3 find the equation of the parabola. But k 6 so p 3 6 3.