if the distance between (na,nb) (a,b) is three times the distance between (4a,4b) and (a,b) Show that - Maths - Coordinate Geometry

Question

if the distance between (na,nb) & (a,b) is three times the
distance between (4a,4b) and (a,b) Show that n is 10 or -8

Varun.Rawat · Accepted Answer

Let Ana,nb and Ba,b be the given points
 AB = na-a2+nb-b2 = a2n-12+b2n-12 = a2+b2n-12Let C4a,4b and Da,b be the given points
CD = 4a-a2+4b-b2 = 9a2+9b2 = 3a2+b2Now, AB = 3 CD⇒a2+b2n-12 = 3 × 3a2+b2⇒a2+b2n-12 = 81a2+b2⇒n-12 = 81⇒n-1 = ±9⇒n = 10  or  n = -8

if the distance between (na,nb) & (a,b) is three times the distance between (4a,4b) and (a,b). Show that n is 10 or -8