Question

If Land L2 are the length of the segments of any focal chord of the parabola y2 = x, then  is equal to

Solution

Correct option is

4

Any point on the parabola is P(at2, 2at)

Where S(a, 0) is the focus of the parabola. So

   

If PQ if a focal chord, then 

So that   

and .

SIMILAR QUESTIONS

Q1

Shortest distance of the point (0, c) from the parabola y = x2where  is

Q2

The length of the intercept on the normal at the point (at2, 2at) of the parabola y2 = 4ax made by the circle which is described on the focal distance of the given point as diameter is 

Q3

A line bisecting the ordinate PN of a point P(at2, 2at), t > 0, on the parabola y2 = 4ax is drawn parallel to the axis to meet the curve at Q. If NQ meets the tangent at the vertex at the point T, then the coordinates of T are.

Q4

If P, Q, R are three points on a parabola y2 = 4ax whose ordinates are in geometrical progression, then the tangents at and R meet on

Q5

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 

Q6

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

Q7

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

Q8

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