Misc 8 - Chapter 11 Class 11 Conic Sections (Important Question)

Last updated at April 16, 2024 by

Misc 8 - An equilateral triangle is inscribed in parabola - Parabola - Triangle in parabola problem

Misc 8 - Chapter 11 Class 11 Conic Sections - Part 2
Misc 8 - Chapter 11 Class 11 Conic Sections - Part 3
Misc 8 - Chapter 11 Class 11 Conic Sections - Part 4

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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.