Question

Find the locus of middle point of chord y2 = 4ax drawn through vertex.

Solution

Correct option is

y2 = 2ax

Let mid-point of the chord be (h, k) then equation of chord in mid-point from is

           ky – 2a(x + h) = k2 – 4ah

As all these chords pass through the vertex hence it must satisfy (0, 0)

          0 – 2i(0 + h) = k2 – 4ah

             4ah – 2ah = k2

                         k2 = 2ah

Thus required locus is a parabola y2 = 2ax.

SIMILAR QUESTIONS

Q1

Axis of the parabola x2 – 4x – 3+ 10 = 0 is  

Q2

The equation of the latus rectum of the parabola x2 + 4x + 2= 0 is 

Q3

x – 2 = t2y = 2t are the parameter equations of the parabola 

Q4

The equation  represents a parabola if  is

Q5

t1’ and ‘t2’ are two points on the parabola y2 = 4x. If the chord joining them is a normal to the parabola at ‘t1’ then

Q6

The vertex of the parabola y2 = 8x is at the center of a circle and the parabola cuts the circle at the ends of its latus rectum. Then the equation of the circle is

Q7

Find the equation of the parabola whose focus is (1, 1) and the directrix is x + y + 1 = 0.

Q8

If the line 2x + 3y = 1 touch the parabola y2 = 4ax at the pointP. Find the focal distance of the point P.

Q9

Find the angle between the tangents of the parabola y2 = 8x, which are drawn from the point (2, 5).

Q10

Find the locus of the mid-point of the chords of the parabola y2 = 4ax which subtend a right angle at the vertex of the parabola.