Question

# The locus of the point (a cos^{3} q, a sin^{3} q) is

- x
^{2/3} – y^{2/3} = a^{2/3} - x
^{2/3} + y^{2/3} = a^{2/3} - x
^{2/3} + y^{2/3} = a^{3/2} - x
^{3/2} + y^{2/3} = a^{3/2}

^{2/3}– y^{2/3}= a^{2/3}^{2/3}+ y^{2/3}= a^{2/3}^{2/3}+ y^{2/3}= a^{3/2}^{3/2}+ y^{2/3}= a^{3/2}Hint:

### Here we have to give the locus of the (a cos^{3} q, a sin^{3} q). Here x and y point are given so put this value in options and find which one satisfy the equation.

## The correct answer is: x^{2/3} + y^{2/3} = a^{2/3}

### Here we have to find the correct equation where locus of the point is given.

Firstly, we have locus which is (a cos^{3} q, a sin^{3} q)

So, x = a cos^{3}q and y = a sin^{3}q

We have, (1)

+ =

LHS

=> (a cos^{3} q) + (a sin^{3} q)

=> ( q) + (sin^{2} q)

=> (( q) + (sin^{2} q))

So, it is not equal to RHS, it is wrong option

(2)

+ =

LHS =

=> +

=> ( cos^{2} q ) + ( sin^{2} q )

=> (cos^{2} q ) + (sin^{2} q )

=> x 1 [ since, (cos^{2} x ) + (sin^{2} x ) = 1 ]

=>

It is not equal to RHS, it is wrong option.

(3)

+ =

LHS=

=> -

=> ( cos^{2} q) - ( sin^{2} q)

=> (cos^{2} q) -(sin^{2} q)

It is not equal to RHS, it is wrong option.

(4)

+ =

LHS=

=> +

=> ( cos^{2} q) + (sin^{2} q)

=> (cos^{2} q) + (sin^{2} q)

=> x 1 [ since, (cos^{2} x) + (sin^{2} 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.

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