If two tangents drawn from the point `(alpha,beta)` to the parabola `y^2=4x` are such that the slope of one tangent is double of the other, then prove that `alpha=2/9beta^2`.

If two tangents drawn from the point (a,b) to the parabola y^2=4x be such that the slope of one tangent is 3 times of the other then

If two tangents drawn from the point P (h,k) to the parabola y^2=8x are such that the slope of one of the tangent is 3 times the slope of the other , then the locus of point P is

The slopes of tangents drawn from a point (4, 10) to parabola y^2=9x are

Find the locus of point P, if two tangents are drawn from it to the parabola y ^(2) = 4x such that the slope of one tangent is three times the slope of other.

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.

The locus of the point such that normals drawn at the point of contact of the tangents drawn from the point to the parabola, are such that the slope of one is double the slope of the other is : (A) y^2 = 9/2 ax (B) x^2 = 4ay (C) y^2 = 9/4 ax (D) x^2 = 9/4 ay

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

(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 .