Question

Find equation of parabola calculator helps in determining the equation of a parabola with given:

a) Focus and directrix.
b) Vertex and axis of symmetry.
c) Intercept and slope.
d) Tangent and normal.

Answer 1

The equation of a parabola can be determined based on different given information: Focus and directrix, Vertex and axis of symmetry, Intercept and slope, Tangent and normal.

Step-by-step explanation:

The equation of a parabola can be determined based on different given information:

a) Focus and directrix:

Let the focus be (h,k). The equation of the parabola can be written in the form (x-h)^2 = 4p(y-k), where p is the distance between the focus and directrix.

b) Vertex and axis of symmetry:

Let the vertex be (h,k). The equation of the parabola can be written in the form y-k = a(x-h)^2, where a is a constant that determines the width and direction of the parabola.

c) Intercept and slope:

Let the intercepts be (x1, y1) and (x2, y2). The equation of the parabola can be written in the form (y-y1) = m(x-x1)(x-x2), where m is the slope of the parabola.

d) Tangent and normal:

Let the tangent and normal lines to the parabola have slopes m1 and m2, respectively, at the point of tangency. The equation of the parabola can be written in the form y = mx + c, where c is a constant.