Question

Through the vertex O of parabola y2 = 4x, chords OP and OQ are drawn at right angles to one another. The locus of the middle point of PQ is

Solution

Correct option is

y2 = 2x – 8

y2 = 4x = 4ax say   …. (1)

 a = 1,  let   P = (t12, 2t1) : Q(t22, 2t2),

slope of OP = 

Since .

Let  be the middle point of chord PQ. Then

        

  

 is y2 = 2x – 8.

SIMILAR QUESTIONS

Q1

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Q2

Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 – 5xy + 6y2) = 0 represents

Q3

The pints of intersection of the two ellipse x2 + 2y2 – 6x – 12y + 23 = 0 and 4x2 + 2y2 – 20x – 12y + 35 = 0.

Q4

The tangent at any point P of the hyperbola  makes an intercept of length p between the point of contact and the transverse axis of the hyperbola, p1p2 are the lengths of the perpendiculars drawn from the foci on the normal at P, then

Q5

The length of chord of contact of the tangents drawn from the point (2, 5) to the parabola y2 = 8x, is 

Q6

The locus of a point whose some of the distance from the origin and the line x = 2 is 4 units, is

Q7

The length of the subnormal to the parabola y2 = 4ax at any point is equal to

Q8

The slope of the normal at the point (at2, 2at) of parabola y2 = 4ax  is

Q9

Equation of locus of a point whose distance from point (a, 0) is equal to its distance from y-axis is

Q10

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