Last updated at May 29, 2018 by Teachoo

Transcript

Misc 8 An equilateral triangle is inscribed in the parabola y2 = 4ax, where one vertex is at the vertex of the parabola. Find the length of the side of the triangle. Let length of equilateral triangle be s Hence OA = OB = AB = s Here, OC AB So, OCA = OCB = 90 And AC = BC So, AC = BC = 2 AC = BC = 2 We find coordinates of point B Now, in right triangle OBC Using Pythagoras theorem (Hypotenuse)2 = (Height)2 + (Base)2 (OB)2 = (OC)2 + (BC)2 s2 = (OC)2 + 2 2 s2 = (OC)2 + 2 4 s2 2 4 = (OC)2 4 2 2 4 = (OC)2 3 2 4 = (OC)2 (OC)2 = 3 2 4 OC = 3 2 4 OC = 3 2 Hence coordinate of point B is B( , ) Now, point B lies on parabola So, it must satisfy its equation Putting x = 3 2 , y = 2 in equation of parabola y2 = 4ax 2 2 = 4a( 3 2 ) 2 4 = 4a( 3 2 ) 2 = 4 4a( 3 2 ) s = 8 a Hence, side of equilateral triangle = 8 3 a

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 9 years. He provides courses for Maths and Science at Teachoo.