Show that the length of the chord of contact of the tangents drawn from `(x_1,y_1)` to the parabola `y^2=4ax` is `1/asqrt[(y_1^2-4ax_1)(y_1^2+4a^2)]`

Shoe that the length of the chord of contact of tangents drawn from (x_(1),y_(1)), to the parabola y^(2)=4ax is (1)/(a)sqrt((y_(1)^(2)-4ax_(1))(y_(1)^(2)+4a^(2)))

Angle between tangents drawn from the point (1, 4) to the parabola y^2 = 4ax is :

What is the length of the focal distance from the point P(x_(1),y_(1)) on the parabola y^(2) =4ax ?

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)

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)

Show that the sum of the ordinate of end of any chord of a system of paralel chords of the parabola y^(2)=4ax 1 is constant.

Area of the triangle formed by the tangents from (x_(1),y_(1)) to the parabola y^(2)=4ax and its chord of contact is ((y_(1)^(2)-4ax_(1))^((3)/(2)))/(2a)=(S_(11)^((3)/(2)))/(2a)

If the tangents at (x_(1),y_(1)) and (x_(2),y_(2)) to the parabola y^(2)=4ax meet at (x_(3),y_(3)) then