Home
Class 11
MATHS
Find the equation of set of points P suc...

Find the equation of set of points P such that `P A^2+P B^2=2k^2`, where A and B are the points `(3, 4, 5)`and `(-1, 3, -7)`, respectively.

Text Solution

AI Generated Solution

To find the equation of the set of points \( P \) such that \( PA^2 + PB^2 = 2k^2 \), where \( A(3, 4, 5) \) and \( B(-1, 3, -7) \), we will follow these steps: ### Step 1: Define the coordinates of point \( P \) Let the coordinates of point \( P \) be \( (x, y, z) \). ### Step 2: Write the distance formulas Using the distance formula, we can express \( PA^2 \) and \( PB^2 \): - The distance \( PA \) from \( P \) to \( A \) is given by: ...
Promotional Banner

Topper's Solved these Questions

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT|Exercise MISCELLANEOUS EXERCISE|6 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT|Exercise EXERCISE 12.1|4 Videos

  • INTRODUCTION TO THREE DIMENSIONAL GEOMETRY

    NCERT|Exercise EXERCISE 12.2|5 Videos

  • CONIC SECTIONS

    NCERT|Exercise EXERCISE 11.1|15 Videos

  • LIMITS AND DERIVATIVES

    NCERT|Exercise EXERCISE 13.3|8 Videos

Similar Questions

Explore conceptually related problems

Find the equation of the set of points P such that PA^(2)+PB^(2)=2k^(2) where A,B are the points (3,4,5) (-1,3,-7) respectively

The locus of a point P which moves such that PA^(2)-PB^(2)=2k^(2) where A and B are (3,4 5) and (-1,3,-7) respectively is

Find the locus of Pquad if quad PA^(2)+PB^(2)=2k^(2) where A and B are points (3,4,5) and (-1,3,7).

Find the equation of the set of the points P such that is distances from the points A(3,4,-5) and B(-1,2,4) are equal.

Find the equation of the set of the points P such that its distances from the points A(3,4,-5) and B are equal.

Find the equation of the set of points p such that its distance from the points A(3,4,-5) and B(-2,1,4) are equal

Find the equation of the set of points P which moves so that its distances from the points A(3,4,-5) and B(-2,1,4) are equal.

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 P A^2+P B^2=k^2 , where k is a constant.

A point P(x,y,z) is such that 3PA=2PB where AandB are the point (1,3,4) and (1,-2,-1), irrespectivley. Find the equation to the locus of the point P and verify that the locus is a sphere.