Find the equation of sets of point P such that its distance from the points A(3,4,-5) B(-2,1,4) are equal - Maths - Introduction to Three Dimensional Geometry

Question

Find the equation of sets of point P such that its distance from
the points A(3,4,-5) B(-2,1,4) are equal

Manbar Singh · Accepted Answer

Solution :

Let P x, y, z be the point which is equidistant from A 3, 4, -5  and  B -2, 1, 4Then,  we have  AP = BP⇒ x - 32 + y - 42 + z + 52 = x + 22 + y - 12 + z - 42using distance formula d = x2 - x12 + y2 - y12 + z2 - z12⇒ x-32 + y-42 + z+52 = x+22 + y-12 + z-42  on squaringx2+9-6x+y2+16-8y+z2+25+10z = x2+4+4x+y2+1-2y+z2+16-8z⇒ 9-6x+16-8y+25+10z = 4+4x+1-2y+16-8z⇒ -6x-8y+10z+50 = 4x-2y-8z+21⇒ -10x-6y+18z+29 = 0⇒ 10x + 6y - 18z - 29 = 0