Question 14 (iv) - Tangents and Normals (using Differentiation) - Chapter 6 Class 12 Application of Derivatives
Last updated at April 16, 2024 by Teachoo
Tangents and Normals (using Differentiation)
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Tangents and Normals (using Differentiation)
Last updated at April 16, 2024 by Teachoo
Question 14 Find the equations of the tangent and normal to the given curves at the indicated points: (iv) π¦=π₯2 ππ‘ (0, 0) Given Curve is π¦=π₯^2 Differentiating w.r.t.π₯ ππ¦/ππ₯=2π₯ We know that Slope of tangent is ππ¦/ππ₯ Given point is (0 , 0) Slope of tangent at (0 , 0) γππ¦/ππ₯βγ_((0 , 0) )=2(0) =0 We know that Slope of tangent Γ Slope if Normal =β1 0 Γ Slope if Normal =β1 Slope if Normal =(β1)/( 0) Equation of tangent at (0 , 0) & having Slope zero is (π¦β0)=0(π₯β0) We know that Equation of line at (π₯1 , π¦1)& having Slope m is π¦βπ¦1=π(π₯βπ₯1) Finding equation of tangent & normal Now Equation of line at (π₯1 , π¦1) & having Slope m is π¦βπ¦1=π(π₯βπ₯1) Equation of tangent at (0, 0) & Slope 0 is (π¦β0)=0(π₯β0) π¦β0=0 π=π Equation of Normal at (0, 0) & Slope (β1)/0 is (π¦β0)=1/0 (π₯β0) 0 Γ (π¦β0)=1(π₯β0) 0=π₯β0 π=π