Find the distance between the points: `(i) P(-6,7)` and`Q(-1,-5)` `(ii)R(a+b , a-b)` and `S(a-b,-a-b)` `(iii) A(a t1 ,2a t_1)` and `B(a t2 ,2a t_2)`

Find the distance between the following pairs of points : (i) (2,3),(4,1) (ii) (-5,-7),(-1,3) (iii) (a,b),(-a,-b)

Find the distance between the following pairs of points : (i) (2, 3), (4, 1) (ii) (– 5, 7), (– 1, 3) (iii) (a, b), (– a, – b)

Find the area of the triangle whose vertices are (6,\ 3),\ (-3,\ 5) and (4,\ -2) (ii) (a t1 2,\ 2a t_1),\ (a t2 2,\ 2a t_2) and (a t3 2,\ 2a t_3) (iii) (a ,\ c+a),\ (a ,\ c) and (-a ,\ c-a)

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

Find the value of the products: (4a^2+3b)(4a^2+3b)a t\ a=1,\ b=2.

The vertices of a triangle are [a t_1t_2,a(t_1 +t_2)] , [a t_2t_3,a(t_2 +t_3)] , [a t_3t_1,a(t_3 +t_1)] Then the orthocenter of the triangle is: (a) (-a, a(t_1+t_2+t_3)-at_1t_2t_3) (b) (-a, a(t_1+t_2+t_3) + a(t_1t_2t_3) (c) (a, a(t_1+t_2+t_3)+at_1t_2t_3) (d) (a, a(t_1+t_2+t_3)-at_1t_2t_3)

The vertices of a triangle are [a t_1t_2,a(t_1 +t_2)] , [a t_2t_3,a(t_2 +t_3)] , [a t_3t_1,a(t_3 +t_1)] Then the orthocenter of the triangle is (a) (-a, a(t_1+t_2+t_3)-at_1t_2t_3) (b) (-a, a(t_1+t_2+t_3)+at_1t_2t_3) (c) (a, a(t_1+t_2+t_3)+at_1t_2t_3) (d) (a, a(t_1+t_2+t_3)-at_1t_2t_3)

Match te columns (1) a-s, b-t, c-r, d-p (2) a-t, b-q, c-r, d-p (3) a-t, b-r, c-q, d-p (4) a-t, b-r, c-p, d-q

Figure given here shows the variation of velocity of a particle with time. Find the following: (i) Displacement during the time intervals. (a) 0 to 2 sec., (b) 2 to 4 sec. and (c) 4 to 7 sec (ii) Accelerations at (a)t = 1 sec, (b) t = 3 sec. and (c)t = 6 sec. (iii) Average acceleration (a) between t = 0 to t = 4 sec. (b) between t = 0 to t = 7 sec. (iv) Average velocity during the motion.

If int_0^1 (e^t dt)/(t+1)=a, then evaluate int_(b-1)^b (e^t dt)/(t-b-1)