Pair of Tangents, Chord of Contact and Chord with Midpoint of a Parabola

IMPORTANT

Pair of Tangents, Chord of Contact and Chord with Midpoint of a Parabola: Overview

This topic covers concepts, such as Midpoint Chord of a Parabola, Length of Chord of Contact to a Parabola, Diameter of a Parabola, Chord of Contact to a Parabola, Equation of the Polar of a Point with Respect to a Parabola, etc.

Important Questions on Pair of Tangents, Chord of Contact and Chord with Midpoint of a Parabola

MEDIUM
IMPORTANT

Consider the parabola y2=4x and hyperbola x29-y216=1. Tangents are drawn from a point P to the parabola y2=4x, the chord of contact of these tangents touches the hyperbola x29-y216=1. The locus of point P is a conic whose eccentricity is e, then 4e2 is equal to

MEDIUM
IMPORTANT

The locus of the mid-points of the chords of the parabola x2=4py having slope m is a

EASY
IMPORTANT

From a point A-12,λ, two tangents are drawn to the parabola y2=2x, which touches the parabola at P & Q, then chord PQ will always pass through -

MEDIUM
IMPORTANT

Locus of mid-point of chords of parabola x2+4ay=0, that pass through the point 3a,-4a is

HARD
IMPORTANT

If y=mx bisect two chords of y2=4x from (4,4), then m can't be

HARD
IMPORTANT

The locus of the mid-points of the chords of the parabola y2=4ax, which passes through the origin is

MEDIUM
IMPORTANT

From the point (4,6), a pair of tangent lines are drawn to the parabola y2=8x. Find the area of the triangle formed by these pair of tangent lines and the chord of contact of the point (4,6).

HARD
IMPORTANT

If the chord of contact of tangents from a point P to the parabola y2=4ax touches the parabola x2=4by, then find the locus of P.

HARD
IMPORTANT

Consider the chords of the parabola y2=4x which touches the hyperbola x2-y2=1. A conic section is formed on tracing the locus of the point of intersection of the tangents drawn to the parabola at the extremities of such chords. If λ represents the length of the conic section's latus rectum, then λ is

HARD
IMPORTANT

From a variable point P on the tangent at the vertex of the parabola y2=2x, a line is drawn perpendicular to the chord of contact. These variable lines always pass through a fixed point, whose x-coordinate is

MEDIUM
IMPORTANT

Tangents are drawn from any point on the directrix of y2=16x to the parabola. If the locus of the midpoint of chords of contact is a parabola, then its length (in units) of the latus rectum is

EASY
IMPORTANT

If two distinct chords of a parabola y2=4ax passing through (a, 2a) are bisected by the line x + y = 1, and 4a is a natural number, then the maximum length of the Latus rectum is

MEDIUM
IMPORTANT

From the point -1, 2 tangent lines are drawn to the parabola y2=4x . If area of triangle formed by the chord of contact and the tangents is 2N, then N=

EASY
IMPORTANT

If P is a point on the parabola y2=8x and A is the point (1,0), then the locus of the midpoint of the line segment AP is

MEDIUM
IMPORTANT

The length of the common chord of the parabolas y2=x and x2=y and is

HARD
IMPORTANT

The locus of the middle points of the chords of the parabola y2=4ax, which passes through the origin is

HARD
IMPORTANT

Equation of chord of the parabola y2=16x whose mid point is (1, 1), is

HARD
IMPORTANT

Locus of midpoint of any focal chord of y2=4ax is

HARD
IMPORTANT

Locus of mid point of any focal chord of y2=4ax is