Question

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 

Solution

Correct option is

Let the coordinate of A, B, C be (ti2, 2ti)i = 1, 2, 3 respectively. The tangents at A and B are

         t1y = x t12  and   t2y = x t22

which intersect at x = t1t2, y = t1 + t2

so the vertices are P(t1t2t1 + t2), Q(t2t3t2 + t3) and R(t1t3t1+ t3)

                           

                               

                               

SIMILAR QUESTIONS

Q1

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 

Q2

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.

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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  

Q8

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