Question

find equation of evolute of parabola x^2=4ay​

Answer 1

Center

$(0,0)$

Vertices

$( - 1,0)(1,0)$

Answer 2

Given: parabola x^2 = 4 ay

To find: evolute of the given parabola

Solution:

The directrix of the parabola

x^2 = 4ay

having y-axis as its axis, passes through (0, -a), and has the equation

y + a = 0

The focus of the parabola

x^2 = -4ay

having y-axis as its axis

passes through (0, a), and has the equation

y - a = 0.

The evolute of a curve (blue parabola) is the locus of all its centers of curvature (red). The evolute of a curve (in this case, an ellipse) is the envelope of its normals.