Question

If `x=a^(2) cos3 theta and y=b^(2)sin3 theta`, then
A. `(x^(2))/(a)+(y^(2))/(b)=1`
B. `((x^(2))/(a^(2)))^(1//3)+((y)/(b^(2)))^(1//3)=1`
C. `((x^(2))/(a^(2)))^(2//3)+((y^(2))/(b^(2)))^(2//3)=1`
D. `((x)/(a^(2)))^(2//3)+((y)/(b^(2)))^(2//3)=1`

Answer 1

Correct Answer - D
Given, `x=a^(2)cos^(3) theta and y=b^(2)sin^(3) theta`.
`implies(x)/(a^(2))=cos^(3)theta and (y)/(b^(2))=sin^(3)theta`
`implies ((x)/(a^(2)))^(2//3)=cos^(2)theta,((y)/(b^(2)))^(2//3)=sin^(2)theta`.
`sin^(2)theta+cos^(2)theta=((x)/(a^(2)))^(2//3)+((y)/(b^(2)))^(2//3)`
`:. ((x)/(a^(2)))^(2//3)+((y)/(b^(2)))^(2//3)=1`