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)

Find the equation of the straight lines passing through the following pair of point: (0,0)a n d\ (2,-2)dot

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 equations t the straight lines passing through the point (2,3) and inclined at an angle of 45^0 to the line \ 3x+y-5=0.

Find the equation of t he straight line through the given point P and having the given slope m if P(-1, -5), m=(-6)/(11)

The equation of straight line passing through (-a ,0) and making a triangle with the axes of area T is (a) 2T x+a^2y+2a T=0 (b) 2T x-a^2y+2a T=0 (c) 2T x-a^2y-2a T=0 (d)none of these

Find the equation of normal to the curves x=t^2, y=2t+1 at point

Find the equations of the tangent and the normal to the curve x=a t^2,\ \ y=2a t at t=1 .

Determine the equation of straight line which is tangent at one point and normal at any point of the curve x=3t^2 , y=2t^3

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.