Q. 175.0( 3 Votes )

Find the locus of P if PA2 + PB2 = 2k2, where A and B are the points (3, 4, 5) and (-1, 3, -7).

Answer :

Given: Points are A(3, 4, 5) and B(-1, 3, -7)


To find: the locus of point P which moves in such a way that PA2 + PB2 = 2k2


Let the required point P(x, y, z)


Formula used:


The distance between any two points (a, b, c) and (m, n, o) is given by,



Therefore,


The distance between P(x, y, z) and A(3, 4, 5) is PA,



Distance between P(x, y, z) and B(-1, 3, -7) is PB,




According to question:


PA2 + PB2 = 2k2


(x – 3)2+ (y – 4)2 + (z – 5)2 + (x + 1)2 + (y – 3)2 + (z + 7)2 = 2k2


x2+ 9 – 6x + y2 + 16 – 8y + z2 + 25 – 10z + x2+ 1 + 2x + y2 + 9 – 6y + z2 + 49 + 14z = 2k2


2x2+ 2y2 + 2z2 – 4x – 14y + 4z + 109 = 2k2


2x2+ 2y2 + 2z2 – 4x – 14y + 4z + 109 – 2k2 = 0


Hence locus of point P is 2x2+ 2y2 + 2z2 – 4x – 14y + 4z + 109 – 2k2 = 0


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Understand the Concept of LocusUnderstand the Concept of LocusUnderstand the Concept of Locus57 mins
Lecture on radical axis of 2 circlesLecture on radical axis of 2 circlesLecture on radical axis of 2 circles48 mins
Standard Equation of CircleStandard Equation of CircleStandard Equation of Circle54 mins
Interactive Quiz on Common tangents & angle of intersection of 2 circlesInteractive Quiz on Common tangents & angle of intersection of 2 circlesInteractive Quiz on Common tangents & angle of intersection of 2 circles56 mins
Parametric Equations of Straight lineParametric Equations of Straight lineParametric Equations of Straight line48 mins
Various Forms of Equations of lineVarious Forms of Equations of lineVarious Forms of Equations of line45 mins
Lecture on Common tangents & angle of intersection of 2 circlesLecture on Common tangents & angle of intersection of 2 circlesLecture on Common tangents & angle of intersection of 2 circles56 mins
Interactive Quiz on Centroid, incentre, orthocentre & circumcentreInteractive Quiz on Centroid, incentre, orthocentre & circumcentreInteractive Quiz on Centroid, incentre, orthocentre & circumcentre56 mins
Lecture on Tangents to a CircleLecture on Tangents to a CircleLecture on Tangents to a Circle57 mins
General & parametric form of circleGeneral & parametric form of circleGeneral & parametric form of circle56 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
caricature
view all courses