Question

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

Solution

Correct option is

x = 0

S(a, 0), P(at2, 2at). If (h, k) be mid-point, then

         2h = a(1 + t2), 2k = 2at  or  k = t  

  

or     Y2 = 4AX

Directrix is X = – A  or  .

SIMILAR QUESTIONS

Q1

If a focal chord with positive slope of the parabola y2 = 16xtouches the circle x2 + y2 – 12+ 34 = 0, then m is

Q2

If 2y = x + 24 is a tangent to parabola y2 = 24x, then its distance from parallel normal is

Q3

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.

Q4

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

Q5

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

Q6

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

  

Q7

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) :

Q8

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

Q9

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

Q10

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