If P and Q are two points whose coordinates are `(a t^2,2a t)a n d(a/(t^2),(2a)/t)` respectively and S is the point (a,0). Show that `1/(S P)+1/(s Q)` is independent of t.

If A(at^2, 2at), B((a)/(t^2) , - (2a)/(t)) and C(a, 0) be any three points, show that 1/(AC) + 1/(BC) is independent of t .

If the points (a ,0),(a t1 ^ 2,\ 2a t_1)a n d\ a t2^ 2,\ 2a t_2) are collinear, write the value of t_1t_2dot

Prove that the area of the triangle whose vertices are (t ,t-2),(t+2,t+2)a n d(t+3,t) is independent of tdot

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

If the coordinates of a vartiable point P be (t+(1)/(t), t-(1)/(t)) , where t is the variable quantity, then the locus of P is

P and Q are two distinct points on the parabola, y^2 = 4x with parameters t and t_1 respectively. If the normal at P passes through Q , then the minimum value of t_1 ^2 is

If PS is the bisector of /_Q P R and P T_|_Q R . Show that /_T P S=1/2(/_Q-/_R)dot

P(t_1) and Q(t_2) are the point t_1a n dt_2 on the parabola y^2=4a x . The normals at Pa n dQ meet on the parabola. Show that the middle point P Q lies on the parabola y^2=2a(x+2a)dot

Statement 1 : If a circle S=0 intersects a hyperbola x y=4 at four points, three of them being (2, 2), (4, 1) and (6,2/3), then the coordinates of the fourth point are (1/4,16) . Statement 2 : If a circle S=0 intersects a hyperbola x y=c^2 at t_1,t_2,t_3, and t_3 then t_1-t_2-t_3-t_4=1

The x-coordinates of a point on t line joining the points Q(2,2,1)a n dR(5,1,-2)i s4. Find its z-coordinate.