Question

Consider a parabola y2 = 4ax, the length of focal chord is l and the length of the perpendicular from vertex to the chord is pthen

Solution

Correct option is

l.p2 is constant

Let P(at2, 2at) and  be a focal chord of the parabola

(as t1t2 = –1)

Length of PQ =   

                            

                              

                              

Length of the perpendicular from the vertex (0, 0) on the linePQ whose equation is

            is given by

                           

So that       .

Which is constant.

SIMILAR QUESTIONS

Q1

The tangents at three points A, B, C on the parabola y2 = 4x, taken in pairs intersect at the points Pand R. If  be the areas of the triangles ABC and PQR respectively, then 

Q2

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

Q3

Equation of a common tangent to the curves y2 = 8x and xy = –1 is 

Q4

The tangent at the point P(x1y1) to the parabola y2 = 4ax meets the parabola y2 = 4a(x + b) at Q and R, the coordinates of the mid-point of QR are  

Q5

Tangent are drawn to a parabola from a point T. If P, Q are the points of constant then perpendicular distance from P, T and upon the tangent at the vertex of the parabola are in.

Q6

Chord of the parabola  which subtend right angle at vertex pass through

Q7

The locus of the vertex of the family of parabolas   is