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Chapter 11 Class 11 Conic Sections
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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

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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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.