Question

Hello guys !

Let p be the point (1,0) and Q a point on the locus y² = 8x . the locus of the mid point of PQ is

Answer 1

Let the coordinates of Q be(2t2,4t)

and the mid point of PQ be(h,k)

then h=(2t2+1)/2, k=(4t-0)/2

Eliminating t we get h=(k/2)2+1/2

so the locus is y2-4x+2=0


I hope it's helpful for you

Answer 2

Hi

Solution :-

let the point Q has (h,k ) point .

Then The according to the given p has point (0,1)

let the midpoint of PQ (a,b) then We have to find midpoint of PQ

h +1/2 = a , and k+0 /2 = b

h = 2a -1 , and k = 2b

according to given :-

y² = 8x

so the locus of midpoint of PQ

(2b)² = 8 (2a-1)

4b² = 16a-8

b² = 4a - 2

b² - 4a +2

y² -4x+2 ( change in X and y form)

= y² - 4x+2 Answer

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Hope it's helpful

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