Tangents are drawn from the point `(x_1,y_1)` to the parabola `y^2=4ax` show that the length of their chord of contact is `1/|a|sqrt((y_1^2-4ax_1)(y_1^2+4a^2))`.

(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 .

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

The angle between the tangents drawn from the point (4, 1) to the parabola x^(2)=4y is

Tangent are drawn from the point (-1,2) on the parabola y^2=4x . Find the length that these tangents will intercept on the line x=2.

Tangent are drawn from the point (-1,2) on the parabola y^2=4x . Find the length that these tangents will intercept on the line x=2.

Tangents are drawn at the end points of a normal chord of the parabola y^(2)=4ax . The locus of their point of intersection is

Area of the triangle formed by the tangents from (x_1,y_1) to the parabola y^2 = 4 ax and its chord of contact is (y_1^2-4ax_1)^(3/2)/(2a)=S_11^(3/2)/(2a)

Find the angle between two tangents drawn from the point ( 1,4) to the parabola y^(2) = 12x

Tangent is drawn at the point (-1,1) on the hyperbola 3x^2-4y^2+1=0 . The area bounded by the tangent and the coordinates axes is