If the curve ay + x 2 = 7 and x 3 = y, cut orthogonally at (1, 1), then the value of a is:

(A)1   (B) 0   (C) –6   (D) 6

Slide41.JPG

Slide42.JPG
Slide43.JPG

Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class


Transcript

Question 8 If the curve ay + x2 = 7 and x3 = y, cut orthogonally at (1, 1), then the value of a is: 1 (B) 0 (C) –6 (D) 6 Two curves cut each other orthogonally means the cut each other at right angles And, if two curves cut at right angles, then their tangents are perpendicular at point of intersection Finding Slope of Tangents of both curves at (1, 1) Slope of tangent of First Curve 𝒂𝒚+𝒙=𝟕 Differentiating w.r.t. x a 𝑑𝑦/𝑑𝑥 + 2𝑥 = 0 𝒅𝒚/𝒅𝒙 = (−𝟐𝒙)/𝒂 At (1, 1), putting x = 1, y = 1 𝑑𝑦/𝑑𝑥=(−2(1))/𝑎 𝑑𝑦/𝑑𝑥=(−2)/𝑎 ∴ Slope =(−𝟐)/𝒂 Slope of tangent of Second Curve 𝒙^𝟑 = 𝒚 Differentiating w.r.t. x 3𝑥^2 = 𝑑𝑦/𝑑𝑥 𝒅𝒚/𝒅𝒙 = 𝟑𝒙^𝟐 At (1, 1), putting x = 1, y = 1 𝑑𝑦/𝑑𝑥= 3(1)^2 𝑑𝑦/𝑑𝑥= 3 ∴ Slope =𝟑 Now, Since tangents are perpendicular Product of the two slopes = −1 (−𝟐)/𝒂 × 3 = −1 −6/𝑎 = −1 −6=−𝑎 𝒂=𝟔 Hence, value of 𝑎 is 6 So, the correct answer is (D)

Ask a doubt
Davneet Singh's photo - Co-founder, Teachoo

Made by

Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.