Question

If o is origin and q is a variable point of y^2=x. Find the locus of midpoint of oq

Answer 1

a point on line y² = x

O (0,0)

mid point will be (h,k)

P (a,b)

P lies on y² = x

0 + a/ 2 = h

a = 2h

0 + b/2 = k

b = 2k

y² = x

4k² = 2h

k² = h/2

k = y , h=x

y² = x/2

Locus mid - point is  

2y² - x = 0

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