The base of a triangle is divided into three equal parts. If `t_1, t_2,t_3` are the tangents of the angles subtended by these parts at the opposite vertex, prove that `(1/(t_1)+1/(t_2))(1/(t_2)+1/(t_3))=4(1+1/(t2 2))dot`

The bae of a triangle is divided into three equal parts. If t_(1), t_(2), t_(3) be the tangent sof the angles subtended by these parts at the opposite vertex, prove that : ((1)/(t_(1))+ (1)/(t_(2)))((1)/(t _(1))+(1)/(t _(3)))=4(1+(1)/(t_(1)^(2)))

Find the are of triangle whose vertex are: (at_(1),(a)/(t_(1)))(at_(2),(a)/(t_(2)))(at_(3),(a)/(t_(3)))

lim_(t rarr(1)/(2))(4t^(2)-1)/(8t^(3)-1)

If 't_1' and 't_2' be the ends of a focal chord of the parabola y^2=4ax then t_1t_2 is equal to

If the orthocentre of the triangle formed by the points t_1,t_2,t_3 on the parabola y^2=4ax is the focus, the value of |t_1t_2+t_2t_3+t_3t_1| is

Solve : (t + 2)/(3) + 1/(t + 1) = (t - 3)/(2) - (t - 1)/(6)

The slope of the tangent to the curves x=3t^2+1,y=t^3-1 at t=1 is

If the tangents at t_(1) and t_(2) to a parabola y^2=4ax are perpendicular then (t_(1)+t_(2))^(2)-(t_(1)-t_(2))^(2) =

The locus of the point x=(t^(2)-1)/(t^(2)+1),y=(2t)/(t^(2)+1)