Find the distance between the points(at12° 2 at) and B (at22, 2 at2)

1.	Find the distance between the points(at12° 2 at) and B (at22, 2 at2) (ii) L (a cos α, a sin α) and M (a cos β, a
Answer» The distance between the points can be calculated by distance formula, root[(x2-x1)^2+ (y2-y1)^2] =root[(at^22-at^21)^2+ (2at2-2at1)^2] =root[a^2(t^22-t^21)^2+ 4a^2(t2-t1)^2] =root[a^2(t2-t1)^2(t2+t1)^2+ 4a^2(t2-t1)^2] =root[(t2-t1)^2{a^2(t2+t1)^2+ 4a^2}] a(t2-t1)root ((t2+t1)2+ 4)

Find the distance between the points(at12° 2 at) and B (at22, 2 at2) (ii) L (a cos α, a sin α) and M (a cos β, a

Answer»

The distance between the points can be calculated by distance formula,

root[(x2-x1)^2+ (y2-y1)^2]

=root[(at^22-at^21)^2+ (2at2-2at1)^2]

=root[a^2(t^22-t^21)^2+ 4a^2(t2-t1)^2]

=root[a^2(t2-t1)^2(t2+t1)^2+ 4a^2(t2-t1)^2]

=root[(t2-t1)^2{a^2(t2+t1)^2+ 4a^2}]

a(t2-t1)root ((t2+t1)2+ 4)