- #1
dtl42
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If given two arbitrary points on a parabola, is there anyway to determine an explicit equation for that parabola. I know there are multiple possible parabolas, but how can I find just one of them?
A parabola is a symmetrical U-shaped curve that can be formed by graphing a quadratic equation. It is a type of conic section and is characterized by its vertex, focus, and directrix.
The vertex of a parabola is the point where the curve changes direction. It can be determined by finding the axis of symmetry, which is a vertical line that passes through the vertex. The x-coordinate of the vertex can be found by using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation in standard form.
The focus of a parabola is a fixed point inside the curve that is equidistant from every point on the parabola. It can be found by using the formula (h+k)/2, where h and k are the x and y coordinates of the vertex.
The directrix of a parabola is a line perpendicular to the axis of symmetry that is also equidistant from every point on the curve. It can be found by using the formula y = k - p, where p is the distance between the vertex and focus.
Parabolas are commonly used in physics and engineering to model the trajectory of projectiles, such as projectiles launched from a cannon or a ball thrown in the air. They can also be used to model the shape of satellite dishes, reflectors, and other curved structures in architecture and design.