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