Question

find the evolute of ellipse x^2/a^2+y^2/b^2=1

Answer 1

evolute of this ellipse is origin

Answer 2

Answer:

The equation to the evolute of the ellipse can be written as, $(ax)^2/3-(by)^2/3=(a^2+b^2)^2/3$.

Step-by-step explanation:

• First, consider the center of the curve as $(x',y')$ which correspond to a point (a, cosΦ, b, sinΦ) of the ellipse, then we can write, $x'=a^2-b^2/a$cos^3Φ and $y'=-a^2-b^2/b$sin^3Φ.
• Formula: cos^2Φ+sin^2Φ=1.
• According to the centre (x',y') the evolute of the ellipse can be written as,  $(ax')2/3+(by')2/3=(a^2+b^2)2/3$