Key points to solve the problem:

• Idea of section formula- Let two points A(x₁,y₁) and B(x₂,y₂) forms a line segment. If a point C(x,y) divides line segment AB in ratio of m:n internally, then coordinates of C is given as:

C = when m = n =1 , C becomes the midpoint of AB and C is given as C =

How to approach: To find locus of a point we first assume the coordinate of point to be (h, k) and write a mathematical equation as per the conditions mentioned in question and finally replace (h, k) with (x, y) to get the locus of point.

Let the coordinates of point whose locus is to be determined be (h, k). Name the moving point be C

As, coordinate of mid point is (h,k) {by our assumption},

Let Q(a,b) be the point such that Q lies on curve y² = x

b² = a ……equation 1

According to question C is midpoint of OQ

∵ C = ⇒ C =

∴

Similarly,

Putting values of a and b in equation 1,we have:

Replace (h,k) with (x,y)

Thus, locus of point is: