Last updated at Aug. 9, 2021 by Teachoo

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Misc 24 The points on the curve 9y2 = π₯3, where the normal to the curve makes equal intercepts with the axes are (A) (4,Β±8/3) (B) (4,(β 8)/3) (C) (4,Β±3/8) (D) (Β± 4, 3/8) Since Normal makes equal intercepts with the axes Itβs equation will be π₯/π+π¦/π=1 Putting b = a π/π+π/π=π π₯+π¦=π π=βπ+π β΄ Slope of Normal = β1 Equation of line is π₯/π+π¦/π=1 where a is x βintercept & b is y β intercept Now, finding slope of normal by Differentiation 9y2 = π₯3 Differentiating w.r.t π₯ π(9π¦2)/ππ₯ = π(π₯3)/ππ₯ 9 π(π¦2)/ππ₯ Γ ππ¦/ππ¦=3π₯2 9 π(π¦2)/ππ¦ Γ ππ¦/ππ₯ = 3x2 9(2π¦) Γ ππ¦/ππ₯ = 3x2 ππ¦/ππ₯ = 3π₯2/9(2π¦) π π/π π= ππ/ππ We know that Slope of tangent Γ slope of normal = β1 π₯2/6π¦ Γ Slope of normal = β1 Slope of normal = (βππ)/ππ Since Normal is at point (π,π) Hence, Slope of normal at (β,π) = (βππ)/ππ Now, Slope of Normal = β1 (β6π)/β2=β1 6k = h2 Also, Point (β,π) is on the curve 9y2 =π₯^3 So, (π,π) will satisfy the equation of curve Putting π₯ = h & y = k in equation 9k2 = h3 Now our equations are 6k = h2 β¦(1) 9k2 = h3 β¦(2) From (3) 6k = h2 k = ππ/π Putting value of k in (4) 9k2 = h3 9(β2/6)^2= h3 9(β4/36)=β3 β4/4 = h3 β4/β3 = 4 h = 4 Putting value of h = 4 in (4) 9k2 = h3 9k2 = (4)3 k2 = 64/9 k = Β± β(64/9) k = Β± π/π Hence required point is (h, k) = (4 , (Β±8)/3) Hence correct answer is A

Miscellaneous

Misc 1 (a)
Deleted for CBSE Board 2022 Exams

Misc 1 (b) Important Deleted for CBSE Board 2022 Exams

Misc 2 Important

Misc 3 Important

Misc 4

Misc 5 Important

Misc 6 Important

Misc 7

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11 Important

Misc 12 Important

Misc 13 Important

Misc 14 Important

Misc 15 Important

Misc 16

Misc 17 Important

Misc 18 Important

Misc. 19 (MCQ) Deleted for CBSE Board 2022 Exams

Misc 20 (MCQ) Important

Misc 21 (MCQ) Important

Misc 22 (MCQ)

Misc. 23 (MCQ) Important

Misc 24 (MCQ) Important You are here

Chapter 6 Class 12 Application of Derivatives (Term 1)

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About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.