Tangents are drawn to the parabola `y^2 = 4x` from the point `(1,3)`. The length of chord of contact is

From the point (-1, 2), tangent lines are drawn to the parabola y^2= 4x . Find the equation of the chord of contact. Also find the area of the triangle formed by the chord of contact and the tangents.

(i) Tangents are drawn from the point (alpha, beta) to the parabola y^2 = 4ax . Show that the length of their chord of contact is : 1/|a| sqrt((beta^2 - 4aalpha) (beta^2 + 4a^2)) . Also show that the area of the triangle formed by the tangents from (alpha, beta) to parabola y^2 = 4ax and the chord of contact is (beta^2 - 4aalpha)^(3/2)/(2a) . (ii) Prove that the area of the triangle formed by the tangents at points t_1 and t_2 on the parabola y^2 = 4ax with the chord joining these two points is a^2/2 |t_1 - t_2|^3 .

From the point (-1, -6) two tangents are drawn to the parabola y^(2)= 4x . Then the angle between the tangents is-

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

From the point (-1,2), tangent lines are to the parabola y^(2)=4x . If the area of the triangle formed by the chord of contact and the tangents is A, then the value of A//sqrt(2) is ___________ .

If from a variable point 'P' on the line 2x-y-1=0 pair of tangent's are drawn to the parabola x^(2)=8y then prove that chord of contact passes through a fixed point,also find that point.

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is

Tangents are drawn from the point (-1, 2) to the parabola y^2 =4x The area of the triangle for tangents and their chord of contact is