Question

find the shortest distance of the point (0,c) from parabola y=x2 where c belongs to [0,5]

Answer 1

"The Parabola is defined as ""the set of all points P in a plane equidistant from a fixed line and a fixed point in the plane.""

The fixed line is called the directrix, and the fixed point is called the focus.

Each parabola is, in some form, a graph of a second-degree function and has many properties that are worthy of examination.

Let's begin by looking at the standard form for the equation of a parabola.

The standard form is (x - h)2 = 4p (y - k), where the focus is (h, k + p) and the directrix is y = k - p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of (y - k)2 = 4p (x - h), where the focus is (h + p, k) and the directrix is x = h - p."