Question

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.

Solution

Correct option is

Equation of the line parallel to the axis and bisecting the ordinate PN of the point P(at2, 2at) is y = at which meet the parabola

y2 = 4ax at the point .

Coordinates of N are (at2, 0).

Equation of QN is 

Which meets the tangent at the vertex, = 0, at the point

                            

                                                                       

SIMILAR QUESTIONS

Q1

A point P moves such that the difference between its distance from the origin and from the axis of x is always a constant c. the locus of P is a

Q2

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

Q3

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 

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

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

Q6

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 

Q7

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