Parabola

On comparing with general equation of parabola , we have
Length of latus rectum

The parabola is ... (i)
and tangent with it is ... (ii)
tangent at any point to (i) is given by,

... (iii)
(ii) and (iii) represents same line, therefore they are identical.

Point of contact is (-4, 1)

Given, parametric equation of parabola is



Vertex is (1, 1), length of latus rectum = 4
Clearly, equation of directrix is
.

We are given the equation of the parabola: The length of the latus rectum for this parabola is given by , and it is given that the length of the latus rectum is 6 units, so: The equation of the chord passing through the vertex and the negative end of the latus rectum can be determined using the general property of the parabola. The negative end of the latus rectum is located at the point , which for this parabola is . For a parabola of the form , the equation of the chord through the vertex and the end of the latus rectum can be written as: Thus, the equation of the chord is . Hence, the correct answer is (B).