Maths-
General
Easy

Question

# The locus of the point (a cos3 q, a sin3 q) is

Hint:

## The correct answer is: x2/3 + y2/3 = a2/3

### Here we have to find the correct equation where locus of the point is given.Firstly, we have locus which is (a cos3 q, a sin3 q) So, x = a cos3q and y = a sin3qWe have, (1) + = LHS=> (a cos3 q)  + (a sin3 q) => (  q) + (sin2 q)=>  (( q) + (sin2 q))So, it is not equal to RHS, it is wrong option (2) +  = LHS = => + => ( cos2 q ) + ( sin2 q ) =>  (cos2 q ) + (sin2 q ) =>  x 1 [ since, (cos2 x ) + (sin2 x ) = 1 ]=> It is not equal to RHS, it is wrong option.(3)  +  =  LHS==> -=> ( cos2 q) - ( sin2 q) =>  (cos2 q) -(sin2 q) It is not equal to RHS, it is wrong option.(4) +  = LHS==> +  => ( cos2 q) + (sin2 q) =>  (cos2 q) + (sin2 q) =>  x 1 [ since, (cos2 x) + (sin2 x) = 1]=> Here, LHS = RHS, so it is the correct answer.Therefore, the correct answer is  +  =

In this question, we have to find the correct option, where we are given with Locus point. The locus of points is defined as the set of points that satisfy certain properties. A locus is a set of points, in geometry, which satisfies a given condition or situation for a shape or a figure.