Misc. 23 - Chapter 6 Class 12 Application of Derivatives

Transcript

Misc 23 The normal to the curve 𝑥^2=4𝑦 passing (1, 2) is (𝐴) 𝑥 + 𝑦 = 3 (𝐵) 𝑥 – 𝑦 = 3 (𝐶) 𝑥 + 𝑦 = 1 (𝐷) 𝑥 – 𝑦 = 1 Since (1, 2) lies on normal, it will satisfy its equation Option 1 Equation of Normal is 𝑥+𝑦=3 Putting 𝑥=1 & 𝑦=2 in equation 𝑥+𝑦=3 1+2=3 3=3 Thus, (1 , 2) Satisfy the Equation of Normal Hence 𝑥+𝑦=3 is Required Equation of Normal Option 2 If equation of Normal is 𝑥−𝑦=3 Putting 𝑥=1 & 𝑦=2 in equation 𝑥−𝑦=3 1−2=3 −1=3 But −1≠3 Hence 𝑥−𝑦=3 is not the equation of Normal Option 3 If Equation of Normal is 𝑥+𝑦=1 Putting 𝑥=1 & 𝑦=2 in equation ⇒ 𝑥+𝑦=1 ⇒ 1+2=1 ⇒ 3=1 But, 3≠1 Hence 𝑥+𝑦=1 is not Required Equation of Normal Option 4 If Equation of Normal is 𝑥−𝑦=1 Putting 𝑥=1 & 𝑦=2 in equation ⇒ 𝑥−𝑦=1 ⇒ 1−2=1 ⇒ −1=1 Since −1≠1 Hence 𝑥−𝑦=1 is not Required Equation of Normal Hence Correct Answer is (A)