Question

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

Solution

Correct option is

y2 – 4x + 2 = 0

Any point on the parabola is (at2, 2at), a = 2.

Q is (2t2, 4t) and P is (1, 0).

If (h, k) be the mid-point of PQ, then

     2h = 2t2 + 1, 2= 4t      

  

  Locus is y2 – 4x + 2 = 0. 

SIMILAR QUESTIONS

Q1

PQ is a focal chord of the parabola y2 = 4axO is the origin. Find the coordinates of the centroid, G, of triangle OPQ and hence find the locus of G as PQ varies.

Q2

Find the shortest distance between the circle x2 + y2 – 24y + 128 = 0 and the parabola y2 = 4x.

Q3

The equation of the directrix of the parabola y2 + 4y + 4x + 2 = 0 is  

Q4

If the line x – 1 = 0 is the directrix of the parabola y– ky + 8 = 0, then one of the of the value of k is

  

Q5

Equation of the parabola whose axis is y = x distance from origin to vertex is  and distance form origin to focus is , is (Focus and vertex lie in Ist quadrant) :

Q6

The focal chord of y2 = 16x is tangent to (x – 6)2 + y2 = 2, then the possible values of the slope of this chord, are

Q7

The curve described parametrically by x = t2 + t + 1, y = t2 – + 1 represents.

Q8

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola y2 = 4ax is another parabola with directrix

Q9

If  and the line 2bx + 3cy + 4d = 0 passes through the points of intersection of the parabolas y2 = 4ax and x2 = 4ay, then

   

Q10

Consider the two curves C1 : y2 = 4xC2 : x2 + y2 – 6x + 1 = 0. Then,