If A and B be the points (3,4,5) and (−1,3,−7) respectively. Find the equation of the set of points P such that PA2 +PB2 =K2, where K is a constant
Given coordinates of pointsA and B are (3,4,5) and (−1,3,−7) respectively.
Let the coordinates of point P be (x,y,z).
Given, PA2+PB2=K2
⇒(x−3)2+(y−4)2+(z−5)2+(x+1)2+(y−3)2+(z+7)2=K2
x2−6x+9+y2−8y+16+z2−10z+25+x2+2x+1+y2−6y+9+z2+14z+49=K2
⇒2x2+2y2+2z2−4x−14y+4z+109=K2
⇒2(x2+y2+z2−2x−7y+2z)=K2−109
⇒x2+y2+z2−2x−7y+2z=K2−1092
which is the required equation.