Find The Locus Of Middle Point Of Chord y2 = 4ax drawn Through Vertex.

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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

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Q2

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Q3

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Q4

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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

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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.