Q. 44.3( 26 Votes )

Find the coordinates of a point on y-axis which are at a distance of 5√2 from the point P (3, –2, 5).

Answer :

Let the point on y-axis be A (0, y, 0).

Then, it is given that the distance between the points A (0, y, 0) and P (3, -2, 5) is .


Now, by Distance Formula, we know that the distance between two points P (x1, y1, z1) and Q (x2, y2, z2) is given by .


So, the distance between the points A (0, y, 0) and P (3, -2, 5) is given by





Squaring both sides, we get


(-2 -y)2 + 34 = 25 × 2


(-2 -y)2 = 50 – 34


4 + y2 + (2 × -2 × -y) = 16


y2 + 4y + 4 -16 = 0


y2 + 4y – 12 = 0


y2 + 6y – 2y – 12 = 0


y (y + 6) 2 (y + 6) = 0


(y + 6) (y - 2) = 0


y = -6, y = 2


So, the points (0, 2, 0) and (0, -6, 0) are the required points on the y-axis.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Introduction To Cell DivisionIntroduction To Cell DivisionIntroduction To Cell Division60 mins
Introduction to Rotation & TorqueIntroduction to Rotation & TorqueIntroduction to Rotation & Torque37 mins
Introduction to Ionic EquilibriumIntroduction to Ionic EquilibriumIntroduction to Ionic Equilibrium48 mins
Introduction to ThermodynamicsIntroduction to ThermodynamicsIntroduction to Thermodynamics63 mins
Introduction to Geometrical IsomerismIntroduction to Geometrical IsomerismIntroduction to Geometrical Isomerism57 mins
Everything you need to know about OrthocentreEverything you need to know about OrthocentreEverything you need to know about Orthocentre46 mins
Interactive Quiz on Centroid, incentre, orthocentre & circumcentreInteractive Quiz on Centroid, incentre, orthocentre & circumcentreInteractive Quiz on Centroid, incentre, orthocentre & circumcentre56 mins
Know All About Centroid of Triangle & its PropertiesKnow All About Centroid of Triangle & its PropertiesKnow All About Centroid of Triangle & its Properties56 mins
Introduction to Chemical BondingIntroduction to Chemical BondingIntroduction to Chemical Bonding63 mins
Introduction to free body diagramsIntroduction to free body diagramsIntroduction to free body diagrams49 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