If x=2t+1,`y=1-t^(2)` where `t in R` is a variable,locus of the point P(x,y) is a parabola whose focus is given by

if x and y coordinates of a point P in x-y plane are given by x=(u cos alpha)t,y=(u sin alpha)t-(1)/(2)gt^(2) where t is a aprameter and u,alpha,g the constants.Then the locus of the point P is a parabola then whose vertex is:

The locus of the mid point of the focal radi of a variable point moving on the parabola,y^(2)=8x is a parabola whose-

Let x=t^(2)+t+1,y=t^(2)-t+1, where t>0 The total number of tangents at (1,1) will be:

For the variable t, the locus of the points of intersection of lines x-2y=t and x+2y=(1)/(t) is

For the curve x=t^(2)-1, y=t^(2)-t , the tangent is parallel to X-axis at the point where

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

Find the position of points P(1,3) w.r.t. parabolas y^(2)=4x and x^(2)=8y .

Find the position of points P(1,3) w.r.t. parabolas y^(2)=4x and x^(2)=8y .

Find the locus of the point (t^(2)-t+1,t^(2)+t+1),t in R

For the variable t, the locus of the point of intersection of the lines 3tx-2y+6t=0 and 3x+2ty-6=0 is