# Example 12

Last updated at March 9, 2017 by Teachoo

Last updated at March 9, 2017 by Teachoo

Transcript

Example 12 Find the equation of the set of the points P such that its distances from the points A (3, 4, –5) and B (– 2, 1, 4) are equal. Given A (3, 4, 5) & B ( –2, 1, 4,) Let point P be (x, y, z,) Given PA = PB Calculating PA P (x, y, z) A (3, 4, – 5) PA = x2−x12+y2−y12+z2 −z12 Here, x1 = x, y1 = y, z1 = z x2 = – 2, y2 = 1, z2 = 4 PA = 3−𝑥2+4−𝑦2+−5−𝑍2 = 3−𝑥2+4−𝑦2+5+𝑍2 = 32+𝑥2−23𝑥+42+𝑦2−2×4−𝑦+52+𝑧2+2(5)(𝑧) = 9+𝑥2−6𝑥+16+𝑦2−8𝑦+25+𝑧2+10𝑧 = 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧 9+16+25 = 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧+40 Calculating PB P (x, y, z) B ( –2, 1, 4) PB = x2−x12+y2−y12+z2 −z12 Here, x1 = x, y1 = y, z1 = z x2 = – 2, y2 = 1, z2 = 4 PB = −2−𝑥2+1−𝑦2+4−𝑧2 = 2+𝑥2+1−𝑦2+4−𝑧2 = 22+𝑥2+22𝑥+12+𝑦2−21𝑦+42+𝑧2−2(4)(𝑧) = 4+𝑥2+4𝑥+1+𝑦2−2𝑦+16+𝑧2−8𝑧 = 𝑥2+𝑦2+𝑧2−4𝑥−2𝑦+8𝑧+21 = 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧+40 Now ,given that PA = PB 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧+40 = 𝑥2+𝑦2+𝑧2+4𝑥−2𝑦+8𝑧+21 Squaring both sides 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧+402 = 𝑥2+𝑦2+𝑧2+4𝑥−2𝑦+8𝑧+212 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧+40 = 𝑥2+𝑦2+𝑧2+4𝑥−2𝑦+8𝑧+21 𝑥2+𝑦2+𝑧2−6𝑥−8𝑦+10𝑧+40 – 𝑥2−𝑦2−𝑧2+4𝑥+2𝑦+8𝑧−21=0 𝑥2−𝑥2+𝑦2+𝑦2+𝑧2−𝑧2−6𝑥−4𝑥+8𝑦+2y+10z+8z+40−21=0 0 + 0 + 0 – 10x – 6y + 18z + 29 = 0 – 10x – 6y + 10z + 29 = 0 0 = 10x + 6y – 10z – 29 = 0 10x + 6y – 10z – 29 = 0 which is the required equation

Chapter 12 Class 11 Introduction to Three Dimensional Geometry

Class 11

Important Question for exams Class 11

- Chapter 1 Class 11 Sets
- Chapter 2 Class 11 Relations and Functions
- Chapter 3 Class 11 Trigonometric Functions
- Chapter 4 Class 11 Mathematical Induction
- Chapter 5 Class 11 Complex Numbers
- Chapter 6 Class 11 Linear Inequalities
- Chapter 7 Class 11 Permutations and Combinations
- Chapter 8 Class 11 Binomial Theorem
- Chapter 9 Class 11 Sequences and Series
- Chapter 10 Class 11 Straight Lines
- Chapter 11 Class 11 Conic Sections
- Chapter 12 Class 11 Introduction to Three Dimensional Geometry
- Chapter 13 Class 11 Limits and Derivatives
- Chapter 14 Class 11 Mathematical Reasoning
- Chapter 15 Class 11 Statistics
- Chapter 16 Class 11 Probability

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.