Question

If P1Q1 and P2Q2 are two focal chords of the parabola y2 = 4ax, then the chords P1P2 and Q1Q2 intersect on the

Solution

Correct option is

Directrix

Let P1(at2, 2at), P1(at22, 2at2). Since P1Q1 and P2Q2 are focal chords of y2 = 4ax. Then

           

Equation of P1P2 is

           y(t1 + t2) = 2(x + at1t2)                … (1)

and equation of Q1Q2 is

           

 –y(t1 + t2) = 2(xt1t2 + a)                     … (2)

Now (1) + (2)   x + a = 0                      … (3)

(3) represents directrix. 

SIMILAR QUESTIONS

Q1

If a normal drawn to the parabola y2 = 4ax at the point (a, 2a) meets parabola again on (at2, 2at), then the value of t will be

Q2

If the straight line x + y = 1 touches the parabola y2 – y + x = 0, then the coordinates of the point of contact are

Q3

The angle of intersection between the curves y2 = 4x and x2 = 32y at point (16, 8) is

Q4

The pole of the line lx + mx + n = 0 with respect to the parabola y2 = 4ax is

Q5

Two tangent are drawn from the point (–2, –1) to the parabola y2 = 4x. if  is the angle between them, then 

Q6

The conic represented by the equation  is

Q7

If (4, 0) is the vertex and y-axis, the directrix of a parabola then its focus is

Q8

The straight line y = mx + c touches the parabola y2 = 4a(x + a) if

Q9

The focus of the parabola x2 – 2x – y + 2 = 0 is

Q10

The condition that the line  be a normal to the parabola  

y2 = 4ax is