﻿ The tangents at three points A, B, C on the parabola y2 = 4x, taken in pairs intersect at the points P, Q and R. If  be the areas of the triangles ABC and PQR respectively, then  : Kaysons Education

# The Tangents At Three Points A, B, C on The Parabola y2 = 4x, Taken In Pairs Intersect At The Points P, Q and R. If  be The Areas Of The Triangles ABC and PQR respectively, Then

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## Question

### 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