A parabola is a type of curve that is formed when a plane intersects with a cone at a specific angle. It is a symmetrical shape that resembles the letter "U".
The focus of a parabola is a fixed point on the interior of the parabola that is equidistant from all points on the curve. It is the point where all of the reflected rays converge.
To find the focus of a parabola, you can use the formula (h,k+p), where (h,k) is the vertex of the parabola and p is the distance between the vertex and the focus. You can also use the focus-directrix property, where the focus is located on the axis of symmetry at a distance of p/2 from the vertex.
The directrix of a parabola is a fixed line that is perpendicular to the axis of symmetry and is located on the exterior of the parabola. It is the line that is equidistant from all points on the curve.
To find the directrix of a parabola, you can use the formula y = k - p, where (h,k) is the vertex of the parabola and p is the distance between the vertex and the focus. You can also use the focus-directrix property, where the directrix is located on the axis of symmetry at a distance of -p/2 from the vertex.