Find the slope of a line passing through the following point:`(a t_1^2,2a t_1)a n d\ (a t_2^2,\ 2a t_2)`

Find the slope of a line passing through the following point: \ (-3,2)a n d\ (1,4)

Find the slope of a line passing through the following point: (3,-5)\ a n d\ (1,2)dot

Find the equation of the straight lines passing through the following pair of point: (a t_1, a//t_1) and (a t_2, a//t_2)

Find the equation of the straight lines passing through the following pair of point: (0,-a)a n d\ (a t_2,\ a//t_2)

If t_1 a n d t_2 are roots of eth equation t^2+lambdat+1=0, where lambda is an arbitrary constant. Then prove that the line joining the points (a t1,22a t_1)a d n(a t2,22a t_2) always passes through a fixed point. Also, find the point.

The chord A B of the parabola y^2=4a x cuts the axis of the parabola at Cdot If A-=(a t_1^ 2,2a t_1),B-=(a t_2^2,2a t_2) , and A C : A B=1:3, then prove that t_2+2t_1=0 .

The points (a t_1^2, 2 a t_1),(a t_2^2, 2a t_2) and (a ,0) will be collinear, if

Find the slope of the tangent to the curve x=t^2+3t-8 , y=2t^2-2t-5 at t=2 .

For any real t ,x=1/2(e^t+e^(-t)),y=1/2(e^t-e^(-t)) is a point on the hyperbola x^2-y^2=1 Show that the area bounded by the hyperbola and the lines joining its centre to the points corresponding to t_1a n d-t_1 is t_1dot

Write the next three terms of the following sequences: t_1=2, t_n=t_(n-1)-1,ngt=2