Misc 22 - Normal at (1,1) on 2y + x2 = 3 is - Chapter 6 - Finding equation of tangent/normal when point and curve is given

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  1. Chapter 6 Class 12 Application of Derivatives
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Misc 22 The normal at the point (1,1) on the curve 2𝑦+﷐𝑥﷮2﷯=3 is ﷐𝐴﷯ 𝑥 + 𝑦 = 0 (𝐵) 𝑥 – 𝑦 = 0 (𝐶) 𝑥 + 𝑦 +1 = 0 (𝐷) 𝑥 – 𝑦 = 1 Since (1, 1) lies on normal, it will satisfy its equation Option 1 Equation of Normal is 𝑥+𝑦=0 Putting 𝑥=1 & 𝑦=1 in equation 1 +1=0 2=0 2≠0 ⇒ 𝑥+𝑦=0 is not equation of Normal Option 2 If Equation of Normal is 𝑥−𝑦 = 0 Putting 𝑥=1 & 𝑦=1 in equation ⇒ 𝑥−𝑦=0 ⇒ 1−1=0 ⇒ 0=0 Since Point ﷐1 , 1﷯ Satisfying the Equation of Normal ⇒ Hence, required Equation of Normal is 𝑥−𝑦=0 Option 3 If Equation of Normal is 𝑥+𝑦+1=0 Putting 𝑥=1 & 𝑦=1 in equation ⇒ 𝑥+𝑦+1=0 ⇒ 1+1+1=0 ⇒ 3=0 But 3 ≠ 0 ⇒ 𝑥+𝑦+1=0 is not Required Equation of Normal Option 4 If Equation of Normal is 𝑥−𝑦=1 Putting 𝑥=1 & 𝑦=1 in equation ⇒ 1 −1=1 ⇒ 0=1 But 0 ≠ 1 ⇒ 𝑥−𝑦=1 is not Required Equation of Normal Hence, Correct Answer is (B)

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