‌P(0+r‌cos‌θ,0+r‌sin‌θ)‌ and ‌Q[0+r‌cos(90+θ)‌, ‌ ‌0+r(sin‌90∘+θ)] ‌P(r‌cos‌θ,r‌sin‌θ)‌ and ‌Q(−r‌sin‌θ,r‌cos‌θ) ‌OP⇒y=x‌tan‌θ ‌OQ⇒y=−x‌cot‌θ ‌ Let ‌P(x,y)‌‌⇒‌‌Q=(−x,y) ‌∵‌‌‌
x
3
+‌
y
2
=1 ⇒‌‌2x+3y=6 ⇒‌‌r(2‌cos‌θ+3‌sin‌θ)=6 ‌ and ‌r(−2‌sin‌θ+3‌cos‌θ)‌‌=6 2‌cos‌θ+3‌sin‌θ‌‌=−2‌sin‌θ+3‌cos‌θ ‌5‌sin‌θ=cos‌θ ‌tan‌θ=‌
1
5
‌y=‌
x
5
⇒5y−x=0 ‌ and ‌‌‌5x+y=0 ‌ So, ‌‌‌(5y−x)(5x+y)=0 ‌5(x2−y2)−24xy=0