Question

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 

Solution

Correct option is

Center of the circle is  and the radius is   

Equation of the normal is

          y = –tx + 2at + at2

If p is the length of the perpendicular from the center on the normal

Then 

If 2x is the required intercept

Then    

               

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

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

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