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)`

The area of the triangle formed by the tangents from (1,3) to the circle x^(2)+y^(2)-4x+6y+1=0 and its chord of contact is

The area of the triangle formed by the tangents from (1,3) to the circle x^(2)+y^(2)-4x+6y+1=0 and its 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 .

The area of the triangle formed by two tangents from " (1,1) " to " x^(2)+y^(2)+4x+6y+4=0 " and their chord of contact is :

Prove that the area of triangle formed by the tangents to the parabola y^(2)=4ax from the point (x_(1),y_(1)) and the chord of contact is 1/(2a)(y_(1)^(2)-4ax_(1))^(3//2) sq. units.

Area of the triangle formed by the pair of tangents drawn form (1,1) to x^(2)+2x-y+7=0 and its chord of contact is Delta then (Delta)/(9) is equal to

Area of the triangle formed by the pair of tangents drawn form (1,1) to x^(2)+2x-y+7=0 and its chord of contact is Delta then (Delta)/(9) is equal to