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

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 points: P(-6,7) and Q(-1,-5)R(a+b,a-b) and S(a-b-b)A(at_(1)^(2),2at_(1)) and B(at_(2)^(2),2at_(2))

Find whether the points (-a,-b),[-(s+1)a,-(s+1)b] and [ (t-1)a,(t-1)b] are collinear?

Find whether the points (-a,-b),[-(s+1)a,-(s+1)b] and [ (t-1)a,(t-1)b] are collinear?

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 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 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 normal at the point (b t_(1)^(2), 2b t_(1)) on a parabola meets the parabola again in the point (b t_(2)^(2), 2b t_(2)) then

IF the points A(1+t,1),B(1+2t,3),C(2t+2,2t) are collinear find 't'.

The lineas r = (6 - 6s) a + (4s - 4) b + (4 - 8s) c and r = (2t - 1) a + (4t - 2) b - (2t + 3) c intersect at