Question

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

Solution

Correct option is

Coordinate of point 

Equation of tangent at P, yt = x + at2,

SIMILAR QUESTIONS

Q1

The square of the differences of the slopes of the lines represented by the equation x2(sec2θ – sin2θ) – (2xy tan θ + y2 sin2θ = 0) is 

Q2

The line joining the origin to the points of intersection of x2 + y2 + 2gx + c = 0 and x2 + y2 + 2fy – c = 0 are at right angles, if

Q3

Two of the lines represented by x3 – 6x2y + 3xy2 + dy3 = 0 are perpendicular for   

Q4

If pairs of lines 3x2 – 2pxy – 3y2 = 0 and 5x2 – 2qxy – 5y2 = 0 are such that each pair bisects the angle between the other pair, then pq is equal to

Q5

The line x + y = 1 meets the line represented by the equation y3 –xy2 – 14x2y + 24x3 = 0 at the points ABC. If O is the origin, then

OA2 + OB2 + OC2 is equal to    

Q6

If the area of the triangle formed by the pair of lines 8x2 – 6xy + y2 = 0 and the line 2x + 3y = a is 7, then a is equal to

 

Q7

If p is length of the perpendicular from the origin on the line  are in A.P. then ab is equal to  

Q8

If two of the lines given by the equation ax3 – 9yx2 – y2x + 4y3 = 0 are perpendicular then a is equal to

Q9

The number of straight lines equidistant from three non-collinear points in the plane of the points is equal to

Q10

If the pair of line  intersect on x-axis, then α is equal to –