Pair of Tangents, Chord of Contact and Chord with Midpoint of a Parabola
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
Consider the parabola and hyperbola . Tangents are drawn from a point to the parabola , the chord of contact of these tangents touches the hyperbola . The locus of point is a conic whose eccentricity is , then is equal to

The locus of the mid-points of the chords of the parabola having slope is

From a point , two tangents are drawn to the parabola , which touches the parabola at & , then chord will always pass through -

Locus of mid-point of chords of parabola , that pass through the point is

If bisect two chords of from then can't be

The locus of the mid-points of the chords of the parabola which passes through the origin is

From the point a pair of tangent lines are drawn to the parabola Find the area of the triangle formed by these pair of tangent lines and the chord of contact of the point .

If the chord of contact of tangents from a point to the parabola touches the parabola , then find the locus of .

Consider the chords of the parabola which touches the hyperbola . 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 represents the length of the conic section's latus rectum, then is

Cotyledons are also called-

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

Tangents are drawn from any point on the directrix of 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

If two distinct chords of a parabola passing through are bisected by the line , and is a natural number, then the maximum length of the Latus rectum is

From the point tangent lines are drawn to the parabola . If area of triangle formed by the chord of contact and the tangents is , then

If is a point on the parabola and is the point , then the locus of the midpoint of the line segment is

The length of the common chord of the parabolas and and is

The locus of the middle points of the chords of the parabola which passes through the origin is

Equation of chord of the parabola whose mid point is (1, 1), is

Locus of midpoint of any focal chord of is

Locus of mid point of any focal chord of is
